%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM518+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.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 : Mon Jul 18 08:45:23 EDT 2022

% Result   : Theorem 23.71s 7.11s
% Output   : Proof 224.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM518+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n007.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 : Wed Jul  6 09:04:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.56/0.58          ____       _                          
% 0.56/0.58    ___  / __ \_____(_)___  ________  __________
% 0.56/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.58  
% 0.56/0.58  A Theorem Prover for First-Order Logic
% 0.56/0.58  (ePrincess v.1.0)
% 0.56/0.58  
% 0.56/0.58  (c) Philipp Rümmer, 2009-2015
% 0.56/0.58  (c) Peter Backeman, 2014-2015
% 0.56/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58  Bug reports to peter@backeman.se
% 0.56/0.58  
% 0.56/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58  
% 0.56/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/1.00  Prover 0: Preprocessing ...
% 3.71/1.50  Prover 0: Constructing countermodel ...
% 18.86/5.92  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.10/6.03  Prover 1: Preprocessing ...
% 19.83/6.18  Prover 1: Constructing countermodel ...
% 23.71/7.11  Prover 1: proved (1187ms)
% 23.71/7.11  Prover 0: stopped
% 23.71/7.11  
% 23.71/7.11  No countermodel exists, formula is valid
% 23.71/7.11  % SZS status Theorem for theBenchmark
% 23.71/7.11  
% 23.71/7.11  Generating proof ... found it (size 12257)
% 218.61/170.62  
% 218.61/170.62  % SZS output start Proof for theBenchmark
% 218.61/170.62  Assumed formulas after preprocessing and simplification: 
% 218.61/170.62  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v9 = 0) &  ~ (v8 = 0) &  ~ (v6 = xn) &  ~ (v4 = 0) &  ~ (v3 = 0) &  ~ (xk = xp) &  ~ (xk = sz10) &  ~ (xk = sz00) &  ~ (xp = xm) &  ~ (xp = xn) &  ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(v2, xp) = xk & sdtsldt0(xn, xr) = v6 & doDivides0(xr, v2) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xr, xm) = v5 & doDivides0(xr, xn) = 0 & doDivides0(xp, v7) = 0 & doDivides0(xp, v6) = 0 & doDivides0(xp, v2) = 0 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v9 & sdtlseqdt0(v6, xn) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = 0 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(v6, xm) = v7 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 &  ~ (isPrime0(sz10) = 0) &  ~ (isPrime0(sz00) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v12 = v11 | v10 = sz00 |  ~ (sdtlseqdt0(v13, v14) = v15) |  ~ (sdtasdt0(v10, v12) = v14) |  ~ (sdtasdt0(v10, v11) = v13) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] : (sdtlseqdt0(v20, v21) = v22 & sdtlseqdt0(v11, v12) = v19 & sdtasdt0(v12, v10) = v21 & sdtasdt0(v11, v10) = v20 & aNaturalNumber0(v12) = v18 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & ( ~ (v19 = 0) |  ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) | (v22 = 0 & v15 = 0 &  ~ (v21 = v20) &  ~ (v14 = v13))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v11 = v10 |  ~ (sdtlseqdt0(v13, v14) = v15) |  ~ (sdtlseqdt0(v10, v11) = 0) |  ~ (sdtpldt0(v11, v12) = v14) |  ~ (sdtpldt0(v10, v12) = v13) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] : ((sdtlseqdt0(v17, v18) = v19 & sdtpldt0(v12, v11) = v18 & sdtpldt0(v12, v10) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v16 = 0) | (v19 = 0 & v15 = 0 &  ~ (v18 = v17) &  ~ (v14 = v13)))) | (aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & ( ~ (v17 = 0) |  ~ (v16 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v10 = sz00 |  ~ (sdtsldt0(v14, v10) = v15) |  ~ (sdtsldt0(v11, v10) = v12) |  ~ (sdtasdt0(v13, v11) = v14) |  ? [v16] :  ? [v17] :  ? [v18] : ((doDivides0(v10, v11) = v18 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & ( ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0))) | (sdtasdt0(v13, v12) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v16 = 0) | v17 = v15)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (sdtasdt0(v10, v12) = v14) |  ~ (sdtasdt0(v10, v11) = v13) |  ~ (sdtpldt0(v13, v14) = v15) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] : (sdtasdt0(v19, v10) = v21 & sdtasdt0(v12, v10) = v23 & sdtasdt0(v11, v10) = v22 & sdtasdt0(v10, v19) = v20 & sdtpldt0(v22, v23) = v24 & sdtpldt0(v11, v12) = v19 & aNaturalNumber0(v12) = v18 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & ( ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) | (v24 = v21 & v20 = v15)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (doDivides0(v10, v13) = v14) |  ~ (sdtpldt0(v11, v12) = v13) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] : (doDivides0(v10, v12) = v19 & doDivides0(v10, v11) = v18 & aNaturalNumber0(v12) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & ( ~ (v19 = 0) |  ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 | v10 = sz00 |  ~ (sdtasdt0(v10, v12) = v14) |  ~ (sdtasdt0(v10, v11) = v13) |  ~ (aNaturalNumber0(v10) = 0) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (sdtasdt0(v12, v10) = v18 & sdtasdt0(v11, v10) = v17 & aNaturalNumber0(v12) = v16 & aNaturalNumber0(v11) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0) | ( ~ (v18 = v17) &  ~ (v14 = v13))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (sdtpldt0(v10, v12) = v14) |  ~ (sdtpldt0(v10, v11) = v13) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] : (sdtpldt0(v12, v10) = v19 & sdtpldt0(v11, v10) = v18 & aNaturalNumber0(v12) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & ( ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) | ( ~ (v19 = v18) &  ~ (v14 = v13))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (sdtasdt0(v13, v12) = v14) |  ~ (sdtasdt0(v10, v11) = v13) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] : (sdtasdt0(v11, v12) = v18 & sdtasdt0(v10, v18) = v19 & aNaturalNumber0(v12) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & ( ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) | v19 = v14))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) |  ~ (sdtpldt0(v10, v11) = v13) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] : (isPrime0(v12) = v18 & doDivides0(v12, v19) = v20 & doDivides0(v12, v11) = v23 & doDivides0(v12, v10) = v22 & iLess0(v14, v1) = v21 & sdtasdt0(v10, v11) = v19 & aNaturalNumber0(v12) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & ( ~ (v21 = 0) |  ~ (v20 = 0) |  ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) | v23 = 0 | v22 = 0))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) |  ~ (sdtpldt0(v10, v11) = v13) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] : (sdtpldt0(v11, v12) = v18 & sdtpldt0(v10, v18) = v19 & aNaturalNumber0(v12) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & ( ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) | v19 = v14))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 | v10 = sz00 |  ~ (sdtsldt0(v11, v10) = v12) |  ~ (sdtasdt0(v10, v13) = v11) |  ? [v14] :  ? [v15] :  ? [v16] : (( ~ (v14 = 0) & aNaturalNumber0(v13) = v14) | (doDivides0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (sdtmndt0(v11, v10) = v12) |  ~ (sdtpldt0(v10, v13) = v11) |  ? [v14] :  ? [v15] :  ? [v16] : (( ~ (v14 = 0) & aNaturalNumber0(v13) = v14) | (sdtlseqdt0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 | v10 = sz00 |  ~ (sdtsldt0(v11, v10) = v12) |  ~ (sdtasdt0(v10, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (doDivides0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (sdtmndt0(v11, v10) = v12) |  ~ (sdtpldt0(v10, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (sdtlseqdt0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v10 = sz00 |  ~ (sdtlseqdt0(v11, v12) = v13) |  ~ (sdtasdt0(v11, v10) = v12) |  ? [v14] :  ? [v15] : (aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (doDivides0(v10, v12) = v13) |  ~ (doDivides0(v10, v11) = 0) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : (doDivides0(v11, v12) = v17 & aNaturalNumber0(v12) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (sdtlseqdt0(v10, v12) = v13) |  ~ (sdtlseqdt0(v10, v11) = 0) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : (sdtlseqdt0(v11, v12) = v17 & aNaturalNumber0(v12) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v12 = 0 |  ~ (doDivides0(v10, v11) = v12) |  ~ (sdtasdt0(v10, v13) = v11) |  ? [v14] :  ? [v15] : (( ~ (v14 = 0) & aNaturalNumber0(v13) = v14) | (aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v12 = 0 |  ~ (sdtlseqdt0(v10, v11) = v12) |  ~ (sdtpldt0(v10, v13) = v11) |  ? [v14] :  ? [v15] : (( ~ (v14 = 0) & aNaturalNumber0(v13) = v14) | (aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtsldt0(v13, v12) = v11) |  ~ (sdtsldt0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (doDivides0(v13, v12) = v11) |  ~ (doDivides0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (iLess0(v13, v12) = v11) |  ~ (iLess0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtmndt0(v13, v12) = v11) |  ~ (sdtmndt0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtlseqdt0(v13, v12) = v11) |  ~ (sdtlseqdt0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtasdt0(v13, v12) = v11) |  ~ (sdtasdt0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtpldt0(v13, v12) = v11) |  ~ (sdtpldt0(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v10 = sz00 |  ~ (sdtsldt0(v11, v10) = v12) |  ~ (sdtasdt0(v10, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : ((v14 = 0 & aNaturalNumber0(v12) = 0) | (doDivides0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (doDivides0(v10, v13) = 0) |  ~ (sdtpldt0(v11, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (doDivides0(v10, v12) = v18 & doDivides0(v10, v11) = v17 & aNaturalNumber0(v12) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v17 = 0) |  ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0) | v18 = 0))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtmndt0(v11, v10) = v12) |  ~ (sdtpldt0(v10, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : ((v14 = 0 & aNaturalNumber0(v12) = 0) | (sdtlseqdt0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0))))) &  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = v10 |  ~ (iLess0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (sdtlseqdt0(v10, v11) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = sz00 |  ~ (sdtlseqdt0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (doDivides0(v10, v11) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (sdtlseqdt0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (sdtlseqdt0(v11, v10) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0) | (v15 = 0 &  ~ (v11 = v10))))) &  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (isPrime0(v12) = v11) |  ~ (isPrime0(v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (aNaturalNumber0(v12) = v11) |  ~ (aNaturalNumber0(v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (sdtasdt0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (sdtasdt0(v11, v10) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0) | v15 = v12))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (sdtasdt0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (aNaturalNumber0(v12) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0) | v15 = 0))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (sdtpldt0(v11, v10) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0) | v15 = v12))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (aNaturalNumber0(v12) = v15 & aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0) | v15 = 0))) &  ! [v10] :  ! [v11] : (v11 = v10 | v11 = sz10 |  ~ (isPrime0(v10) = 0) |  ~ (doDivides0(v11, v10) = 0) |  ? [v12] : (( ~ (v12 = 0) & aNaturalNumber0(v11) = v12) | ( ~ (v12 = 0) & aNaturalNumber0(v10) = v12))) &  ! [v10] :  ! [v11] : (v11 = v10 |  ~ (sdtlseqdt0(v10, v11) = 0) |  ? [v12] :  ? [v13] :  ? [v14] : (sdtlseqdt0(v11, v10) = v14 & aNaturalNumber0(v11) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v14 = 0) |  ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v10] :  ! [v11] : (v11 = sz00 | v10 = sz00 |  ~ (sdtasdt0(v10, v11) = sz00) |  ? [v12] :  ? [v13] : (aNaturalNumber0(v11) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v10] :  ! [v11] : (v11 = sz00 |  ~ (sdtpldt0(v10, v11) = sz00) |  ? [v12] :  ? [v13] : (aNaturalNumber0(v11) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v10] :  ! [v11] : (v11 = 0 | v10 = sz10 | v10 = sz00 |  ~ (isPrime0(v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] : ((v14 = 0 & v13 = 0 &  ~ (v12 = v10) &  ~ (v12 = sz10) & doDivides0(v12, v10) = 0 & aNaturalNumber0(v12) = 0) | ( ~ (v12 = 0) & aNaturalNumber0(v10) = v12))) &  ! [v10] :  ! [v11] : (v11 = 0 | v10 = sz10 | v10 = sz00 |  ~ (sdtlseqdt0(sz10, v10) = v11) |  ? [v12] : ( ~ (v12 = 0) & aNaturalNumber0(v10) = v12)) &  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (sdtlseqdt0(v10, v10) = v11) |  ? [v12] : ( ~ (v12 = 0) & aNaturalNumber0(v10) = v12)) &  ! [v10] :  ! [v11] : (v10 = sz00 |  ~ (sdtpldt0(v10, v11) = sz00) |  ? [v12] :  ? [v13] : (aNaturalNumber0(v11) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v10] :  ! [v11] : ( ~ (doDivides0(v10, v11) = 0) |  ? [v12] :  ? [v13] :  ? [v14] : ((v14 = v11 & v13 = 0 & sdtasdt0(v10, v12) = v11 & aNaturalNumber0(v12) = 0) | (aNaturalNumber0(v11) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0))))) &  ! [v10] :  ! [v11] : ( ~ (sdtlseqdt0(v10, v11) = 0) |  ? [v12] :  ? [v13] :  ? [v14] : ((v14 = v11 & v13 = 0 & sdtpldt0(v10, v12) = v11 & aNaturalNumber0(v12) = 0) | (aNaturalNumber0(v11) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0))))) &  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(sz10, v10) = v11) |  ? [v12] :  ? [v13] : (sdtasdt0(v10, sz10) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v12 = 0) | (v13 = v10 & v11 = v10)))) &  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(sz00, v10) = v11) |  ? [v12] :  ? [v13] : (sdtasdt0(v10, sz00) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v12 = 0) | (v13 = sz00 & v11 = sz00)))) &  ! [v10] :  ! [v11] : ( ~ (sdtpldt0(sz00, v10) = v11) |  ? [v12] :  ? [v13] : (sdtpldt0(v10, sz00) = v13 & aNaturalNumber0(v10) = v12 & ( ~ (v12 = 0) | (v13 = v10 & v11 = v10)))) &  ! [v10] : (v10 = sz10 | v10 = sz00 |  ~ (aNaturalNumber0(v10) = 0) |  ? [v11] : (isPrime0(v11) = 0 & doDivides0(v11, v10) = 0 & aNaturalNumber0(v11) = 0)))
% 218.61/170.70  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 218.61/170.70  | (1)  ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0) &  ~ (all_0_3_3 = xn) &  ~ (all_0_5_5 = 0) &  ~ (all_0_6_6 = 0) &  ~ (xk = xp) &  ~ (xk = sz10) &  ~ (xk = sz00) &  ~ (xp = xm) &  ~ (xp = xn) &  ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_7_7, xp) = xk & sdtsldt0(xn, xr) = all_0_3_3 & doDivides0(xr, all_0_7_7) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xr, xm) = all_0_4_4 & doDivides0(xr, xn) = 0 & doDivides0(xp, all_0_2_2) = 0 & doDivides0(xp, all_0_3_3) = 0 & doDivides0(xp, all_0_7_7) = 0 & doDivides0(xp, xm) = all_0_1_1 & doDivides0(xp, xn) = all_0_0_0 & sdtlseqdt0(all_0_3_3, xn) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = 0 & sdtlseqdt0(xp, xm) = all_0_5_5 & sdtlseqdt0(xp, xn) = all_0_6_6 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(all_0_3_3, xm) = all_0_2_2 & sdtasdt0(xn, xm) = all_0_7_7 & sdtpldt0(all_0_9_9, xp) = all_0_8_8 & sdtpldt0(xn, xm) = all_0_9_9 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 &  ~ (isPrime0(sz10) = 0) &  ~ (isPrime0(sz00) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v2 = v1 | v0 = sz00 |  ~ (sdtlseqdt0(v3, v4) = v5) |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) | (v12 = 0 & v5 = 0 &  ~ (v11 = v10) &  ~ (v4 = v3))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (sdtlseqdt0(v3, v4) = v5) |  ~ (sdtlseqdt0(v0, v1) = 0) |  ~ (sdtpldt0(v1, v2) = v4) |  ~ (sdtpldt0(v0, v2) = v3) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 &  ~ (v8 = v7) &  ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v0 = sz00 |  ~ (sdtsldt0(v4, v0) = v5) |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ (sdtpldt0(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (doDivides0(v0, v3) = v4) |  ~ (sdtpldt0(v1, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ (aNaturalNumber0(v0) = 0) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | ( ~ (v8 = v7) &  ~ (v4 = v3))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | ( ~ (v9 = v8) &  ~ (v4 = v3))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | v9 = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_0_8_8) = v11 & sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | v13 = 0 | v12 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | v9 = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v3) = v1) |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 | v0 = sz00 |  ~ (sdtlseqdt0(v1, v2) = v3) |  ~ (sdtasdt0(v1, v0) = v2) |  ? [v4] :  ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (doDivides0(v0, v2) = v3) |  ~ (doDivides0(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (sdtlseqdt0(v0, v2) = v3) |  ~ (sdtlseqdt0(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (doDivides0(v0, v1) = v2) |  ~ (sdtasdt0(v0, v3) = v1) |  ? [v4] :  ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (sdtlseqdt0(v0, v1) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ? [v4] :  ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (doDivides0(v3, v2) = v1) |  ~ (doDivides0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (iLess0(v3, v2) = v1) |  ~ (iLess0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~ (sdtlseqdt0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (doDivides0(v0, v3) = 0) |  ~ (sdtpldt0(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0) | v8 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (iLess0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = sz00 |  ~ (sdtlseqdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (sdtlseqdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | (v5 = 0 &  ~ (v1 = v0))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (isPrime0(v2) = v1) |  ~ (isPrime0(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1) |  ~ (aNaturalNumber0(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0))) &  ! [v0] :  ! [v1] : (v1 = v0 | v1 = sz10 |  ~ (isPrime0(v0) = 0) |  ~ (doDivides0(v1, v0) = 0) |  ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtlseqdt0(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) |  ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ? [v2] :  ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ? [v2] :  ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0] :  ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 |  ~ (isPrime0(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 &  ~ (v2 = v0) &  ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) &  ! [v0] :  ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 |  ~ (sdtlseqdt0(sz10, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (sdtlseqdt0(v0, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) &  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ? [v2] :  ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0] :  ! [v1] : ( ~ (doDivides0(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))) &  ! [v0] :  ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ? [v2] :  ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ? [v2] :  ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) &  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ? [v2] :  ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ (aNaturalNumber0(v0) = 0) |  ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 218.93/170.72  |
% 218.93/170.72  | Applying alpha-rule on (1) yields:
% 218.93/170.72  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 218.93/170.72  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | v9 = v4)))
% 218.93/170.72  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))
% 218.93/170.72  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0))
% 218.93/170.72  | (6) doDivides0(xr, xn) = 0
% 218.93/170.72  | (7) sdtlseqdt0(xm, xp) = 0
% 218.93/170.72  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (iLess0(v3, v2) = v1) |  ~ (iLess0(v3, v2) = v0))
% 218.93/170.72  | (9) aNaturalNumber0(xp) = 0
% 218.93/170.72  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~ (sdtlseqdt0(v3, v2) = v0))
% 218.93/170.72  | (11)  ! [v0] :  ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 |  ~ (sdtlseqdt0(sz10, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 218.93/170.72  | (12) aNaturalNumber0(xm) = 0
% 218.93/170.72  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2)))
% 218.93/170.72  | (14)  ~ (all_0_5_5 = 0)
% 218.93/170.72  | (15)  ~ (isPrime0(sz00) = 0)
% 218.93/170.72  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0))
% 218.93/170.72  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))))
% 218.93/170.72  | (18)  ~ (all_0_0_0 = 0)
% 218.93/170.72  | (19)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ? [v2] :  ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 218.93/170.72  | (20)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = sz00 |  ~ (sdtlseqdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0))))
% 218.93/170.72  | (21)  ! [v0] :  ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))))
% 218.93/170.72  | (22)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ? [v2] :  ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 218.93/170.73  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (doDivides0(v0, v3) = 0) |  ~ (sdtpldt0(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0) | v8 = 0)))
% 218.93/170.73  | (24)  ! [v0] :  ! [v1] : ( ~ (doDivides0(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))))
% 218.93/170.73  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0)))
% 218.93/170.73  | (26) aNaturalNumber0(sz00) = 0
% 218.93/170.73  | (27)  ~ (xk = sz00)
% 218.93/170.73  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1) |  ~ (aNaturalNumber0(v2) = v0))
% 218.93/170.73  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (sdtlseqdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | (v5 = 0 &  ~ (v1 = v0)))))
% 218.93/170.73  | (30)  ! [v0] :  ! [v1] : (v1 = v0 | v1 = sz10 |  ~ (isPrime0(v0) = 0) |  ~ (doDivides0(v1, v0) = 0) |  ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 218.93/170.73  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | ( ~ (v9 = v8) &  ~ (v4 = v3)))))
% 218.93/170.73  | (32)  ~ (isPrime0(sz10) = 0)
% 218.93/170.73  | (33) doDivides0(xp, xm) = all_0_1_1
% 218.93/170.73  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0)))
% 218.93/170.73  | (35)  ~ (all_0_3_3 = xn)
% 218.93/170.73  | (36) sdtlseqdt0(xn, xp) = 0
% 218.93/170.73  | (37) doDivides0(xp, all_0_7_7) = 0
% 218.93/170.73  | (38)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (sdtlseqdt0(v0, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 218.93/170.73  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v3) = v1) |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))))
% 218.93/170.73  | (40) sdtpldt0(xn, xm) = all_0_9_9
% 218.93/170.73  | (41)  ! [v0] :  ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 |  ~ (isPrime0(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 &  ~ (v2 = v0) &  ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 218.93/170.73  | (42)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ? [v2] :  ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 218.93/170.73  | (43) doDivides0(xr, all_0_7_7) = 0
% 218.93/170.73  | (44) sdtlseqdt0(all_0_3_3, xn) = 0
% 218.93/170.73  | (45) sdtasdt0(all_0_3_3, xm) = all_0_2_2
% 218.93/170.73  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))))
% 218.93/170.73  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (sdtlseqdt0(v0, v1) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ? [v4] :  ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0)))))
% 218.93/170.73  | (48)  ~ (xk = xp)
% 218.93/170.73  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 218.93/170.73  | (50)  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ? [v2] :  ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 218.93/170.73  | (51) doDivides0(xp, xn) = all_0_0_0
% 218.93/170.74  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (doDivides0(v0, v1) = v2) |  ~ (sdtasdt0(v0, v3) = v1) |  ? [v4] :  ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0)))))
% 218.93/170.74  | (53) isPrime0(xp) = 0
% 218.93/170.74  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_0_8_8) = v11 & sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | v13 = 0 | v12 = 0)))
% 218.93/170.74  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))
% 218.93/170.74  | (56)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ? [v2] :  ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 218.93/170.74  | (57) sdtpldt0(all_0_9_9, xp) = all_0_8_8
% 218.93/170.74  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (sdtlseqdt0(v0, v2) = v3) |  ~ (sdtlseqdt0(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))
% 218.93/170.74  | (59) doDivides0(xr, xm) = all_0_4_4
% 218.93/170.74  | (60)  ~ (all_0_6_6 = 0)
% 218.93/170.74  | (61) aNaturalNumber0(sz10) = 0
% 218.93/170.74  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v2 = v1 | v0 = sz00 |  ~ (sdtlseqdt0(v3, v4) = v5) |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) | (v12 = 0 & v5 = 0 &  ~ (v11 = v10) &  ~ (v4 = v3)))))
% 218.93/170.74  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (doDivides0(v0, v2) = v3) |  ~ (doDivides0(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0))))
% 218.93/170.74  | (64) sdtlseqdt0(xp, xm) = all_0_5_5
% 218.93/170.74  | (65) sdtsldt0(xn, xr) = all_0_3_3
% 218.93/170.74  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v0 = sz00 |  ~ (sdtsldt0(v4, v0) = v5) |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 218.93/170.74  | (67) sdtsldt0(all_0_7_7, xp) = xk
% 218.93/170.74  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ (sdtpldt0(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) | (v14 = v11 & v10 = v5))))
% 218.93/170.74  | (69)  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ? [v2] :  ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 218.93/170.74  | (70) doDivides0(xp, all_0_3_3) = 0
% 218.93/170.74  | (71) sdtlseqdt0(xp, xn) = all_0_6_6
% 218.93/170.74  | (72)  ~ (all_0_1_1 = 0)
% 218.93/170.74  | (73)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtlseqdt0(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) |  ~ (v3 = 0) |  ~ (v2 = 0))))
% 218.93/170.74  | (74) sdtlseqdt0(xk, xp) = 0
% 218.93/170.74  | (75)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (isPrime0(v2) = v1) |  ~ (isPrime0(v2) = v0))
% 218.93/170.74  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0) | v9 = v4)))
% 218.93/170.74  | (77)  ~ (sz10 = sz00)
% 218.93/170.74  | (78)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (iLess0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0))))
% 218.93/170.75  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (doDivides0(v3, v2) = v1) |  ~ (doDivides0(v3, v2) = v0))
% 218.93/170.75  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (doDivides0(v0, v3) = v4) |  ~ (sdtpldt0(v1, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0))))
% 218.93/170.75  | (81) doDivides0(xp, all_0_2_2) = 0
% 218.93/170.75  | (82)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ (aNaturalNumber0(v0) = 0) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | ( ~ (v8 = v7) &  ~ (v4 = v3)))))
% 218.93/170.75  | (83)  ~ (xk = sz10)
% 218.93/170.75  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v4 = 0)))))
% 218.93/170.75  | (85) doDivides0(xr, xk) = 0
% 218.93/170.75  | (86) isPrime0(xr) = 0
% 218.93/170.75  | (87)  ~ (xp = xn)
% 218.93/170.75  | (88) aNaturalNumber0(xr) = 0
% 218.93/170.75  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 | v0 = sz00 |  ~ (sdtlseqdt0(v1, v2) = v3) |  ~ (sdtasdt0(v1, v0) = v2) |  ? [v4] :  ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0))))
% 218.93/170.75  | (90) sdtlseqdt0(xr, xk) = 0
% 218.93/170.75  | (91) aNaturalNumber0(xn) = 0
% 218.93/170.75  | (92)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ (aNaturalNumber0(v0) = 0) |  ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 218.93/170.75  | (93)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2)))
% 218.93/170.75  | (94)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (sdtlseqdt0(v3, v4) = v5) |  ~ (sdtlseqdt0(v0, v1) = 0) |  ~ (sdtpldt0(v1, v2) = v4) |  ~ (sdtpldt0(v0, v2) = v3) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 &  ~ (v8 = v7) &  ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0)))))
% 218.93/170.75  | (95)  ~ (xp = xm)
% 218.93/170.75  | (96) sdtasdt0(xn, xm) = all_0_7_7
% 218.93/170.75  |
% 218.93/170.75  | Instantiating formula (79) with xp, xm, all_0_1_1, 0 and discharging atoms doDivides0(xp, xm) = all_0_1_1, yields:
% 218.93/170.75  | (97) all_0_1_1 = 0 |  ~ (doDivides0(xp, xm) = 0)
% 218.93/170.75  |
% 218.93/170.75  | Using (86) and (32) yields:
% 218.93/170.75  | (98)  ~ (xr = sz10)
% 218.93/170.75  |
% 218.93/170.75  | Using (53) and (32) yields:
% 218.93/170.75  | (99)  ~ (xp = sz10)
% 218.93/170.75  |
% 218.93/170.75  | Using (86) and (15) yields:
% 218.93/170.75  | (100)  ~ (xr = sz00)
% 218.93/170.75  |
% 218.93/170.75  | Using (53) and (15) yields:
% 218.93/170.75  | (101)  ~ (xp = sz00)
% 218.93/170.75  |
% 218.93/170.75  | Instantiating formula (24) with all_0_7_7, xr and discharging atoms doDivides0(xr, all_0_7_7) = 0, yields:
% 218.93/170.75  | (102)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = all_0_7_7 & v1 = 0 & sdtasdt0(xr, v0) = all_0_7_7 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 218.93/170.75  |
% 218.93/170.75  | Instantiating formula (24) with xn, xr and discharging atoms doDivides0(xr, xn) = 0, yields:
% 218.93/170.75  | (103)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = xn & v1 = 0 & sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 218.93/170.75  |
% 218.93/170.75  | Instantiating formula (24) with all_0_7_7, xp and discharging atoms doDivides0(xp, all_0_7_7) = 0, yields:
% 218.93/170.75  | (104)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = all_0_7_7 & v1 = 0 & sdtasdt0(xp, v0) = all_0_7_7 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 218.93/170.75  |
% 218.93/170.75  | Instantiating formula (63) with all_0_1_1, xm, all_0_7_7, xp and discharging atoms doDivides0(xp, all_0_7_7) = 0, doDivides0(xp, xm) = all_0_1_1, yields:
% 218.93/170.76  | (105) all_0_1_1 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_7_7, xm) = v3 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (63) with all_0_1_1, xm, all_0_2_2, xp and discharging atoms doDivides0(xp, all_0_2_2) = 0, doDivides0(xp, xm) = all_0_1_1, yields:
% 218.93/170.76  | (106) all_0_1_1 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_2_2, xm) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (63) with all_0_1_1, xm, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, doDivides0(xp, xm) = all_0_1_1, yields:
% 218.93/170.76  | (107) all_0_1_1 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_3_3, xm) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (63) with all_0_0_0, xn, all_0_7_7, xp and discharging atoms doDivides0(xp, all_0_7_7) = 0, doDivides0(xp, xn) = all_0_0_0, yields:
% 218.93/170.76  | (108) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_7_7, xn) = v3 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (63) with all_0_0_0, xn, all_0_2_2, xp and discharging atoms doDivides0(xp, all_0_2_2) = 0, doDivides0(xp, xn) = all_0_0_0, yields:
% 218.93/170.76  | (109) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_2_2, xn) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (63) with all_0_0_0, xn, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, doDivides0(xp, xn) = all_0_0_0, yields:
% 218.93/170.76  | (110) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_3_3, xn) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (73) with xn, all_0_3_3 and discharging atoms sdtlseqdt0(all_0_3_3, xn) = 0, yields:
% 218.93/170.76  | (111) all_0_3_3 = xn |  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (21) with xn, all_0_3_3 and discharging atoms sdtlseqdt0(all_0_3_3, xn) = 0, yields:
% 218.93/170.76  | (112)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = xn & v1 = 0 & sdtpldt0(all_0_3_3, v0) = xn & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (73) with xk, xr and discharging atoms sdtlseqdt0(xr, xk) = 0, yields:
% 218.93/170.76  | (113) xr = xk |  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(xk, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (73) with xp, xk and discharging atoms sdtlseqdt0(xk, xp) = 0, yields:
% 218.93/170.76  | (114) xk = xp |  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (21) with xp, xm and discharging atoms sdtlseqdt0(xm, xp) = 0, yields:
% 218.93/170.76  | (115)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (21) with xp, xn and discharging atoms sdtlseqdt0(xn, xp) = 0, yields:
% 218.93/170.76  | (116)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xn, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (50) with xm, all_0_3_3 yields:
% 218.93/170.76  | (117) all_0_3_3 = sz00 | xm = sz00 |  ~ (sdtasdt0(all_0_3_3, xm) = sz00) |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (42) with all_0_2_2, xm yields:
% 218.93/170.76  | (118)  ~ (sdtasdt0(sz00, xm) = all_0_2_2) |  ? [v0] :  ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_2_2 = sz00)))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (93) with all_0_2_2, xm, all_0_3_3 and discharging atoms sdtasdt0(all_0_3_3, xm) = all_0_2_2, yields:
% 218.93/170.76  | (119)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(xm, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_2_2))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (25) with all_0_2_2, xm, all_0_3_3 and discharging atoms sdtasdt0(all_0_3_3, xm) = all_0_2_2, yields:
% 218.93/170.76  | (120)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_0_2_2) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (93) with all_0_7_7, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_7_7, yields:
% 218.93/170.76  | (121)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_7_7))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (25) with all_0_7_7, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_7_7, yields:
% 218.93/170.76  | (122)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_0_7_7) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 218.93/170.76  |
% 218.93/170.76  | Instantiating formula (13) with all_0_8_8, xp, all_0_9_9 and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, yields:
% 218.93/170.77  | (123)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_8_8))
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (34) with all_0_8_8, xp, all_0_9_9 and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, yields:
% 218.93/170.77  | (124)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(all_0_9_9) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (54) with all_0_8_8, all_0_9_9, xp, xm, xn and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtpldt0(xn, xm) = all_0_9_9, yields:
% 218.93/170.77  | (125)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(all_0_8_8, all_0_8_8) = v6 & sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (3) with all_0_8_8, all_0_9_9, xp, xm, xn and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtpldt0(xn, xm) = all_0_9_9, yields:
% 218.93/170.77  | (126)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_8_8))
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (13) with all_0_9_9, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_9_9, yields:
% 218.93/170.77  | (127)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_9_9))
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (34) with all_0_9_9, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_9_9, yields:
% 218.93/170.77  | (128)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (92) with xr and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 218.93/170.77  | (129) xr = sz10 | xr = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (92) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 218.93/170.77  | (130) xp = sz10 | xp = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 218.93/170.77  |
% 218.93/170.77  | Instantiating formula (92) with xm and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 218.93/170.77  | (131) xm = sz10 | xm = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xm) = 0 & aNaturalNumber0(v0) = 0)
% 218.93/170.77  |
% 218.93/170.77  | Instantiating (128) with all_12_0_10, all_12_1_11, all_12_2_12 yields:
% 218.93/170.77  | (132) aNaturalNumber0(all_0_9_9) = all_12_0_10 & aNaturalNumber0(xm) = all_12_1_11 & aNaturalNumber0(xn) = all_12_2_12 & ( ~ (all_12_1_11 = 0) |  ~ (all_12_2_12 = 0) | all_12_0_10 = 0)
% 218.93/170.77  |
% 218.93/170.77  | Applying alpha-rule on (132) yields:
% 218.93/170.77  | (133) aNaturalNumber0(all_0_9_9) = all_12_0_10
% 218.93/170.77  | (134) aNaturalNumber0(xm) = all_12_1_11
% 218.93/170.77  | (135) aNaturalNumber0(xn) = all_12_2_12
% 218.93/170.77  | (136)  ~ (all_12_1_11 = 0) |  ~ (all_12_2_12 = 0) | all_12_0_10 = 0
% 218.93/170.77  |
% 218.93/170.77  | Instantiating (127) with all_14_0_13, all_14_1_14, all_14_2_15 yields:
% 218.93/170.77  | (137) sdtpldt0(xm, xn) = all_14_0_13 & aNaturalNumber0(xm) = all_14_1_14 & aNaturalNumber0(xn) = all_14_2_15 & ( ~ (all_14_1_14 = 0) |  ~ (all_14_2_15 = 0) | all_14_0_13 = all_0_9_9)
% 218.93/170.77  |
% 218.93/170.77  | Applying alpha-rule on (137) yields:
% 218.93/170.77  | (138) sdtpldt0(xm, xn) = all_14_0_13
% 218.93/170.77  | (139) aNaturalNumber0(xm) = all_14_1_14
% 218.93/170.77  | (140) aNaturalNumber0(xn) = all_14_2_15
% 218.93/170.77  | (141)  ~ (all_14_1_14 = 0) |  ~ (all_14_2_15 = 0) | all_14_0_13 = all_0_9_9
% 218.93/170.77  |
% 218.93/170.77  | Instantiating (122) with all_16_0_16, all_16_1_17, all_16_2_18 yields:
% 218.93/170.77  | (142) aNaturalNumber0(all_0_7_7) = all_16_0_16 & aNaturalNumber0(xm) = all_16_1_17 & aNaturalNumber0(xn) = all_16_2_18 & ( ~ (all_16_1_17 = 0) |  ~ (all_16_2_18 = 0) | all_16_0_16 = 0)
% 218.93/170.77  |
% 218.93/170.77  | Applying alpha-rule on (142) yields:
% 218.93/170.77  | (143) aNaturalNumber0(all_0_7_7) = all_16_0_16
% 218.93/170.77  | (144) aNaturalNumber0(xm) = all_16_1_17
% 218.93/170.77  | (145) aNaturalNumber0(xn) = all_16_2_18
% 218.93/170.77  | (146)  ~ (all_16_1_17 = 0) |  ~ (all_16_2_18 = 0) | all_16_0_16 = 0
% 218.93/170.77  |
% 218.93/170.77  | Instantiating (121) with all_18_0_19, all_18_1_20, all_18_2_21 yields:
% 218.93/170.77  | (147) sdtasdt0(xm, xn) = all_18_0_19 & aNaturalNumber0(xm) = all_18_1_20 & aNaturalNumber0(xn) = all_18_2_21 & ( ~ (all_18_1_20 = 0) |  ~ (all_18_2_21 = 0) | all_18_0_19 = all_0_7_7)
% 218.93/170.77  |
% 218.93/170.77  | Applying alpha-rule on (147) yields:
% 218.93/170.77  | (148) sdtasdt0(xm, xn) = all_18_0_19
% 218.93/170.77  | (149) aNaturalNumber0(xm) = all_18_1_20
% 218.93/170.77  | (150) aNaturalNumber0(xn) = all_18_2_21
% 218.93/170.77  | (151)  ~ (all_18_1_20 = 0) |  ~ (all_18_2_21 = 0) | all_18_0_19 = all_0_7_7
% 218.93/170.77  |
% 218.93/170.77  | Instantiating (120) with all_20_0_22, all_20_1_23, all_20_2_24 yields:
% 218.93/170.77  | (152) aNaturalNumber0(all_0_2_2) = all_20_0_22 & aNaturalNumber0(all_0_3_3) = all_20_2_24 & aNaturalNumber0(xm) = all_20_1_23 & ( ~ (all_20_1_23 = 0) |  ~ (all_20_2_24 = 0) | all_20_0_22 = 0)
% 218.93/170.77  |
% 218.93/170.77  | Applying alpha-rule on (152) yields:
% 218.93/170.77  | (153) aNaturalNumber0(all_0_2_2) = all_20_0_22
% 218.93/170.77  | (154) aNaturalNumber0(all_0_3_3) = all_20_2_24
% 218.93/170.77  | (155) aNaturalNumber0(xm) = all_20_1_23
% 218.93/170.77  | (156)  ~ (all_20_1_23 = 0) |  ~ (all_20_2_24 = 0) | all_20_0_22 = 0
% 218.93/170.77  |
% 218.93/170.77  | Instantiating (119) with all_22_0_25, all_22_1_26, all_22_2_27 yields:
% 218.93/170.77  | (157) sdtasdt0(xm, all_0_3_3) = all_22_0_25 & aNaturalNumber0(all_0_3_3) = all_22_2_27 & aNaturalNumber0(xm) = all_22_1_26 & ( ~ (all_22_1_26 = 0) |  ~ (all_22_2_27 = 0) | all_22_0_25 = all_0_2_2)
% 218.93/170.77  |
% 218.93/170.77  | Applying alpha-rule on (157) yields:
% 218.93/170.77  | (158) sdtasdt0(xm, all_0_3_3) = all_22_0_25
% 218.93/170.77  | (159) aNaturalNumber0(all_0_3_3) = all_22_2_27
% 218.93/170.77  | (160) aNaturalNumber0(xm) = all_22_1_26
% 218.93/170.78  | (161)  ~ (all_22_1_26 = 0) |  ~ (all_22_2_27 = 0) | all_22_0_25 = all_0_2_2
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (124) with all_24_0_28, all_24_1_29, all_24_2_30 yields:
% 218.93/170.78  | (162) aNaturalNumber0(all_0_8_8) = all_24_0_28 & aNaturalNumber0(all_0_9_9) = all_24_2_30 & aNaturalNumber0(xp) = all_24_1_29 & ( ~ (all_24_1_29 = 0) |  ~ (all_24_2_30 = 0) | all_24_0_28 = 0)
% 218.93/170.78  |
% 218.93/170.78  | Applying alpha-rule on (162) yields:
% 218.93/170.78  | (163) aNaturalNumber0(all_0_8_8) = all_24_0_28
% 218.93/170.78  | (164) aNaturalNumber0(all_0_9_9) = all_24_2_30
% 218.93/170.78  | (165) aNaturalNumber0(xp) = all_24_1_29
% 218.93/170.78  | (166)  ~ (all_24_1_29 = 0) |  ~ (all_24_2_30 = 0) | all_24_0_28 = 0
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (123) with all_26_0_31, all_26_1_32, all_26_2_33 yields:
% 218.93/170.78  | (167) sdtpldt0(xp, all_0_9_9) = all_26_0_31 & aNaturalNumber0(all_0_9_9) = all_26_2_33 & aNaturalNumber0(xp) = all_26_1_32 & ( ~ (all_26_1_32 = 0) |  ~ (all_26_2_33 = 0) | all_26_0_31 = all_0_8_8)
% 218.93/170.78  |
% 218.93/170.78  | Applying alpha-rule on (167) yields:
% 218.93/170.78  | (168) sdtpldt0(xp, all_0_9_9) = all_26_0_31
% 218.93/170.78  | (169) aNaturalNumber0(all_0_9_9) = all_26_2_33
% 218.93/170.78  | (170) aNaturalNumber0(xp) = all_26_1_32
% 218.93/170.78  | (171)  ~ (all_26_1_32 = 0) |  ~ (all_26_2_33 = 0) | all_26_0_31 = all_0_8_8
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (104) with all_28_0_34, all_28_1_35, all_28_2_36 yields:
% 218.93/170.78  | (172) (all_28_0_34 = all_0_7_7 & all_28_1_35 = 0 & sdtasdt0(xp, all_28_2_36) = all_0_7_7 & aNaturalNumber0(all_28_2_36) = 0) | (aNaturalNumber0(all_0_7_7) = all_28_1_35 & aNaturalNumber0(xp) = all_28_2_36 & ( ~ (all_28_1_35 = 0) |  ~ (all_28_2_36 = 0)))
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (116) with all_30_0_40, all_30_1_41, all_30_2_42 yields:
% 218.93/170.78  | (173) (all_30_0_40 = xp & all_30_1_41 = 0 & sdtpldt0(xn, all_30_2_42) = xp & aNaturalNumber0(all_30_2_42) = 0) | (aNaturalNumber0(xp) = all_30_1_41 & aNaturalNumber0(xn) = all_30_2_42 & ( ~ (all_30_1_41 = 0) |  ~ (all_30_2_42 = 0)))
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (112) with all_32_0_46, all_32_1_47, all_32_2_48 yields:
% 218.93/170.78  | (174) (all_32_0_46 = xn & all_32_1_47 = 0 & sdtpldt0(all_0_3_3, all_32_2_48) = xn & aNaturalNumber0(all_32_2_48) = 0) | (aNaturalNumber0(all_0_3_3) = all_32_2_48 & aNaturalNumber0(xn) = all_32_1_47 & ( ~ (all_32_1_47 = 0) |  ~ (all_32_2_48 = 0)))
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (115) with all_33_0_49, all_33_1_50, all_33_2_51 yields:
% 218.93/170.78  | (175) (all_33_0_49 = xp & all_33_1_50 = 0 & sdtpldt0(xm, all_33_2_51) = xp & aNaturalNumber0(all_33_2_51) = 0) | (aNaturalNumber0(xp) = all_33_1_50 & aNaturalNumber0(xm) = all_33_2_51 & ( ~ (all_33_1_50 = 0) |  ~ (all_33_2_51 = 0)))
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (103) with all_34_0_52, all_34_1_53, all_34_2_54 yields:
% 218.93/170.78  | (176) (all_34_0_52 = xn & all_34_1_53 = 0 & sdtasdt0(xr, all_34_2_54) = xn & aNaturalNumber0(all_34_2_54) = 0) | (aNaturalNumber0(xr) = all_34_2_54 & aNaturalNumber0(xn) = all_34_1_53 & ( ~ (all_34_1_53 = 0) |  ~ (all_34_2_54 = 0)))
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (126) with all_37_0_61, all_37_1_62, all_37_2_63, all_37_3_64, all_37_4_65 yields:
% 218.93/170.78  | (177) sdtpldt0(xm, xp) = all_37_1_62 & sdtpldt0(xn, all_37_1_62) = all_37_0_61 & aNaturalNumber0(xp) = all_37_2_63 & aNaturalNumber0(xm) = all_37_3_64 & aNaturalNumber0(xn) = all_37_4_65 & ( ~ (all_37_2_63 = 0) |  ~ (all_37_3_64 = 0) |  ~ (all_37_4_65 = 0) | all_37_0_61 = all_0_8_8)
% 218.93/170.78  |
% 218.93/170.78  | Applying alpha-rule on (177) yields:
% 218.93/170.78  | (178) sdtpldt0(xn, all_37_1_62) = all_37_0_61
% 218.93/170.78  | (179) aNaturalNumber0(xp) = all_37_2_63
% 218.93/170.78  | (180) aNaturalNumber0(xn) = all_37_4_65
% 218.93/170.78  | (181) aNaturalNumber0(xm) = all_37_3_64
% 218.93/170.78  | (182) sdtpldt0(xm, xp) = all_37_1_62
% 218.93/170.78  | (183)  ~ (all_37_2_63 = 0) |  ~ (all_37_3_64 = 0) |  ~ (all_37_4_65 = 0) | all_37_0_61 = all_0_8_8
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (125) with all_39_0_66, all_39_1_67, all_39_2_68, all_39_3_69, all_39_4_70, all_39_5_71, all_39_6_72, all_39_7_73, all_39_8_74 yields:
% 218.93/170.78  | (184) isPrime0(xp) = all_39_5_71 & doDivides0(xp, all_39_4_70) = all_39_3_69 & doDivides0(xp, xm) = all_39_0_66 & doDivides0(xp, xn) = all_39_1_67 & iLess0(all_0_8_8, all_0_8_8) = all_39_2_68 & sdtasdt0(xn, xm) = all_39_4_70 & aNaturalNumber0(xp) = all_39_6_72 & aNaturalNumber0(xm) = all_39_7_73 & aNaturalNumber0(xn) = all_39_8_74 & ( ~ (all_39_2_68 = 0) |  ~ (all_39_3_69 = 0) |  ~ (all_39_5_71 = 0) |  ~ (all_39_6_72 = 0) |  ~ (all_39_7_73 = 0) |  ~ (all_39_8_74 = 0) | all_39_0_66 = 0 | all_39_1_67 = 0)
% 218.93/170.78  |
% 218.93/170.78  | Applying alpha-rule on (184) yields:
% 218.93/170.78  | (185) aNaturalNumber0(xn) = all_39_8_74
% 218.93/170.78  | (186) doDivides0(xp, all_39_4_70) = all_39_3_69
% 218.93/170.78  | (187) aNaturalNumber0(xp) = all_39_6_72
% 218.93/170.78  | (188) iLess0(all_0_8_8, all_0_8_8) = all_39_2_68
% 218.93/170.78  | (189)  ~ (all_39_2_68 = 0) |  ~ (all_39_3_69 = 0) |  ~ (all_39_5_71 = 0) |  ~ (all_39_6_72 = 0) |  ~ (all_39_7_73 = 0) |  ~ (all_39_8_74 = 0) | all_39_0_66 = 0 | all_39_1_67 = 0
% 218.93/170.78  | (190) isPrime0(xp) = all_39_5_71
% 218.93/170.78  | (191) doDivides0(xp, xm) = all_39_0_66
% 218.93/170.78  | (192) sdtasdt0(xn, xm) = all_39_4_70
% 218.93/170.78  | (193) doDivides0(xp, xn) = all_39_1_67
% 218.93/170.78  | (194) aNaturalNumber0(xm) = all_39_7_73
% 218.93/170.78  |
% 218.93/170.78  | Instantiating (102) with all_41_0_75, all_41_1_76, all_41_2_77 yields:
% 218.93/170.78  | (195) (all_41_0_75 = all_0_7_7 & all_41_1_76 = 0 & sdtasdt0(xr, all_41_2_77) = all_0_7_7 & aNaturalNumber0(all_41_2_77) = 0) | (aNaturalNumber0(all_0_7_7) = all_41_1_76 & aNaturalNumber0(xr) = all_41_2_77 & ( ~ (all_41_1_76 = 0) |  ~ (all_41_2_77 = 0)))
% 218.93/170.78  |
% 218.93/170.78  +-Applying beta-rule and splitting (105), into two cases.
% 218.93/170.78  |-Branch one:
% 218.93/170.78  | (196) all_0_1_1 = 0
% 218.93/170.78  |
% 218.93/170.79  	| Equations (196) can reduce 72 to:
% 218.93/170.79  	| (197) $false
% 218.93/170.79  	|
% 218.93/170.79  	|-The branch is then unsatisfiable
% 218.93/170.79  |-Branch two:
% 218.93/170.79  | (72)  ~ (all_0_1_1 = 0)
% 218.93/170.79  | (199)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_7_7, xm) = v3 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 218.93/170.79  |
% 218.93/170.79  	| Instantiating (199) with all_47_0_81, all_47_1_82, all_47_2_83, all_47_3_84 yields:
% 218.93/170.79  	| (200) doDivides0(all_0_7_7, xm) = all_47_0_81 & aNaturalNumber0(all_0_7_7) = all_47_2_83 & aNaturalNumber0(xp) = all_47_3_84 & aNaturalNumber0(xm) = all_47_1_82 & ( ~ (all_47_0_81 = 0) |  ~ (all_47_1_82 = 0) |  ~ (all_47_2_83 = 0) |  ~ (all_47_3_84 = 0))
% 218.93/170.79  	|
% 218.93/170.79  	| Applying alpha-rule on (200) yields:
% 218.93/170.79  	| (201) aNaturalNumber0(xm) = all_47_1_82
% 218.93/170.79  	| (202) aNaturalNumber0(xp) = all_47_3_84
% 218.93/170.79  	| (203)  ~ (all_47_0_81 = 0) |  ~ (all_47_1_82 = 0) |  ~ (all_47_2_83 = 0) |  ~ (all_47_3_84 = 0)
% 218.93/170.79  	| (204) aNaturalNumber0(all_0_7_7) = all_47_2_83
% 219.39/170.79  	| (205) doDivides0(all_0_7_7, xm) = all_47_0_81
% 219.39/170.79  	|
% 219.39/170.79  	+-Applying beta-rule and splitting (114), into two cases.
% 219.39/170.79  	|-Branch one:
% 219.39/170.79  	| (206) xk = xp
% 219.39/170.79  	|
% 219.39/170.79  		| Equations (206) can reduce 48 to:
% 219.39/170.79  		| (197) $false
% 219.39/170.79  		|
% 219.39/170.79  		|-The branch is then unsatisfiable
% 219.39/170.79  	|-Branch two:
% 219.39/170.79  	| (48)  ~ (xk = xp)
% 219.39/170.79  	| (209)  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.79  	|
% 219.39/170.79  		| Instantiating (209) with all_52_0_85, all_52_1_86, all_52_2_87 yields:
% 219.39/170.79  		| (210) sdtlseqdt0(xp, xk) = all_52_0_85 & aNaturalNumber0(xk) = all_52_2_87 & aNaturalNumber0(xp) = all_52_1_86 & ( ~ (all_52_0_85 = 0) |  ~ (all_52_1_86 = 0) |  ~ (all_52_2_87 = 0))
% 219.39/170.79  		|
% 219.39/170.79  		| Applying alpha-rule on (210) yields:
% 219.39/170.79  		| (211) sdtlseqdt0(xp, xk) = all_52_0_85
% 219.39/170.79  		| (212) aNaturalNumber0(xk) = all_52_2_87
% 219.39/170.79  		| (213) aNaturalNumber0(xp) = all_52_1_86
% 219.39/170.79  		| (214)  ~ (all_52_0_85 = 0) |  ~ (all_52_1_86 = 0) |  ~ (all_52_2_87 = 0)
% 219.39/170.79  		|
% 219.39/170.79  		+-Applying beta-rule and splitting (110), into two cases.
% 219.39/170.79  		|-Branch one:
% 219.39/170.79  		| (215) all_0_0_0 = 0
% 219.39/170.79  		|
% 219.39/170.79  			| Equations (215) can reduce 18 to:
% 219.39/170.79  			| (197) $false
% 219.39/170.79  			|
% 219.39/170.79  			|-The branch is then unsatisfiable
% 219.39/170.79  		|-Branch two:
% 219.39/170.79  		| (18)  ~ (all_0_0_0 = 0)
% 219.39/170.79  		| (218)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_3_3, xn) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.79  		|
% 219.39/170.79  			| Instantiating (218) with all_57_0_88, all_57_1_89, all_57_2_90, all_57_3_91 yields:
% 219.39/170.79  			| (219) doDivides0(all_0_3_3, xn) = all_57_0_88 & aNaturalNumber0(all_0_3_3) = all_57_2_90 & aNaturalNumber0(xp) = all_57_3_91 & aNaturalNumber0(xn) = all_57_1_89 & ( ~ (all_57_0_88 = 0) |  ~ (all_57_1_89 = 0) |  ~ (all_57_2_90 = 0) |  ~ (all_57_3_91 = 0))
% 219.39/170.79  			|
% 219.39/170.79  			| Applying alpha-rule on (219) yields:
% 219.39/170.79  			| (220)  ~ (all_57_0_88 = 0) |  ~ (all_57_1_89 = 0) |  ~ (all_57_2_90 = 0) |  ~ (all_57_3_91 = 0)
% 219.39/170.79  			| (221) aNaturalNumber0(all_0_3_3) = all_57_2_90
% 219.39/170.79  			| (222) doDivides0(all_0_3_3, xn) = all_57_0_88
% 219.39/170.79  			| (223) aNaturalNumber0(xp) = all_57_3_91
% 219.39/170.79  			| (224) aNaturalNumber0(xn) = all_57_1_89
% 219.39/170.79  			|
% 219.39/170.79  			+-Applying beta-rule and splitting (111), into two cases.
% 219.39/170.79  			|-Branch one:
% 219.39/170.79  			| (225) all_0_3_3 = xn
% 219.39/170.79  			|
% 219.39/170.79  				| Equations (225) can reduce 35 to:
% 219.39/170.79  				| (197) $false
% 219.39/170.79  				|
% 219.39/170.79  				|-The branch is then unsatisfiable
% 219.39/170.79  			|-Branch two:
% 219.39/170.79  			| (35)  ~ (all_0_3_3 = xn)
% 219.39/170.79  			| (228)  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.79  			|
% 219.39/170.79  				| Instantiating (228) with all_62_0_92, all_62_1_93, all_62_2_94 yields:
% 219.39/170.79  				| (229) sdtlseqdt0(xn, all_0_3_3) = all_62_0_92 & aNaturalNumber0(all_0_3_3) = all_62_2_94 & aNaturalNumber0(xn) = all_62_1_93 & ( ~ (all_62_0_92 = 0) |  ~ (all_62_1_93 = 0) |  ~ (all_62_2_94 = 0))
% 219.39/170.79  				|
% 219.39/170.79  				| Applying alpha-rule on (229) yields:
% 219.39/170.79  				| (230) sdtlseqdt0(xn, all_0_3_3) = all_62_0_92
% 219.39/170.79  				| (231) aNaturalNumber0(all_0_3_3) = all_62_2_94
% 219.39/170.80  				| (232) aNaturalNumber0(xn) = all_62_1_93
% 219.39/170.80  				| (233)  ~ (all_62_0_92 = 0) |  ~ (all_62_1_93 = 0) |  ~ (all_62_2_94 = 0)
% 219.39/170.80  				|
% 219.39/170.80  				+-Applying beta-rule and splitting (106), into two cases.
% 219.39/170.80  				|-Branch one:
% 219.39/170.80  				| (196) all_0_1_1 = 0
% 219.39/170.80  				|
% 219.39/170.80  					| Equations (196) can reduce 72 to:
% 219.39/170.80  					| (197) $false
% 219.39/170.80  					|
% 219.39/170.80  					|-The branch is then unsatisfiable
% 219.39/170.80  				|-Branch two:
% 219.39/170.80  				| (72)  ~ (all_0_1_1 = 0)
% 219.39/170.80  				| (237)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_2_2, xm) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.80  				|
% 219.39/170.80  					| Instantiating (237) with all_67_0_95, all_67_1_96, all_67_2_97, all_67_3_98 yields:
% 219.39/170.80  					| (238) doDivides0(all_0_2_2, xm) = all_67_0_95 & aNaturalNumber0(all_0_2_2) = all_67_2_97 & aNaturalNumber0(xp) = all_67_3_98 & aNaturalNumber0(xm) = all_67_1_96 & ( ~ (all_67_0_95 = 0) |  ~ (all_67_1_96 = 0) |  ~ (all_67_2_97 = 0) |  ~ (all_67_3_98 = 0))
% 219.39/170.80  					|
% 219.39/170.80  					| Applying alpha-rule on (238) yields:
% 219.39/170.80  					| (239)  ~ (all_67_0_95 = 0) |  ~ (all_67_1_96 = 0) |  ~ (all_67_2_97 = 0) |  ~ (all_67_3_98 = 0)
% 219.39/170.80  					| (240) aNaturalNumber0(xp) = all_67_3_98
% 219.39/170.80  					| (241) doDivides0(all_0_2_2, xm) = all_67_0_95
% 219.39/170.80  					| (242) aNaturalNumber0(xm) = all_67_1_96
% 219.39/170.80  					| (243) aNaturalNumber0(all_0_2_2) = all_67_2_97
% 219.39/170.80  					|
% 219.39/170.80  					+-Applying beta-rule and splitting (107), into two cases.
% 219.39/170.80  					|-Branch one:
% 219.39/170.80  					| (196) all_0_1_1 = 0
% 219.39/170.80  					|
% 219.39/170.80  						| Equations (196) can reduce 72 to:
% 219.39/170.80  						| (197) $false
% 219.39/170.80  						|
% 219.39/170.80  						|-The branch is then unsatisfiable
% 219.39/170.80  					|-Branch two:
% 219.39/170.80  					| (72)  ~ (all_0_1_1 = 0)
% 219.39/170.80  					| (247)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_3_3, xm) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.80  					|
% 219.39/170.80  						| Instantiating (247) with all_72_0_99, all_72_1_100, all_72_2_101, all_72_3_102 yields:
% 219.39/170.80  						| (248) doDivides0(all_0_3_3, xm) = all_72_0_99 & aNaturalNumber0(all_0_3_3) = all_72_2_101 & aNaturalNumber0(xp) = all_72_3_102 & aNaturalNumber0(xm) = all_72_1_100 & ( ~ (all_72_0_99 = 0) |  ~ (all_72_1_100 = 0) |  ~ (all_72_2_101 = 0) |  ~ (all_72_3_102 = 0))
% 219.39/170.80  						|
% 219.39/170.80  						| Applying alpha-rule on (248) yields:
% 219.39/170.80  						| (249) doDivides0(all_0_3_3, xm) = all_72_0_99
% 219.39/170.80  						| (250)  ~ (all_72_0_99 = 0) |  ~ (all_72_1_100 = 0) |  ~ (all_72_2_101 = 0) |  ~ (all_72_3_102 = 0)
% 219.39/170.80  						| (251) aNaturalNumber0(xp) = all_72_3_102
% 219.39/170.80  						| (252) aNaturalNumber0(all_0_3_3) = all_72_2_101
% 219.39/170.80  						| (253) aNaturalNumber0(xm) = all_72_1_100
% 219.39/170.80  						|
% 219.39/170.80  						+-Applying beta-rule and splitting (108), into two cases.
% 219.39/170.80  						|-Branch one:
% 219.39/170.80  						| (215) all_0_0_0 = 0
% 219.39/170.80  						|
% 219.39/170.80  							| Equations (215) can reduce 18 to:
% 219.39/170.80  							| (197) $false
% 219.39/170.80  							|
% 219.39/170.80  							|-The branch is then unsatisfiable
% 219.39/170.80  						|-Branch two:
% 219.39/170.80  						| (18)  ~ (all_0_0_0 = 0)
% 219.39/170.80  						| (257)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_7_7, xn) = v3 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.80  						|
% 219.39/170.80  							| Instantiating (257) with all_77_0_103, all_77_1_104, all_77_2_105, all_77_3_106 yields:
% 219.39/170.80  							| (258) doDivides0(all_0_7_7, xn) = all_77_0_103 & aNaturalNumber0(all_0_7_7) = all_77_2_105 & aNaturalNumber0(xp) = all_77_3_106 & aNaturalNumber0(xn) = all_77_1_104 & ( ~ (all_77_0_103 = 0) |  ~ (all_77_1_104 = 0) |  ~ (all_77_2_105 = 0) |  ~ (all_77_3_106 = 0))
% 219.39/170.80  							|
% 219.39/170.80  							| Applying alpha-rule on (258) yields:
% 219.39/170.80  							| (259) aNaturalNumber0(all_0_7_7) = all_77_2_105
% 219.39/170.80  							| (260) aNaturalNumber0(xn) = all_77_1_104
% 219.39/170.80  							| (261) doDivides0(all_0_7_7, xn) = all_77_0_103
% 219.39/170.80  							| (262)  ~ (all_77_0_103 = 0) |  ~ (all_77_1_104 = 0) |  ~ (all_77_2_105 = 0) |  ~ (all_77_3_106 = 0)
% 219.39/170.80  							| (263) aNaturalNumber0(xp) = all_77_3_106
% 219.39/170.80  							|
% 219.39/170.80  							+-Applying beta-rule and splitting (109), into two cases.
% 219.39/170.80  							|-Branch one:
% 219.39/170.80  							| (215) all_0_0_0 = 0
% 219.39/170.80  							|
% 219.39/170.80  								| Equations (215) can reduce 18 to:
% 219.39/170.80  								| (197) $false
% 219.39/170.80  								|
% 219.39/170.80  								|-The branch is then unsatisfiable
% 219.39/170.80  							|-Branch two:
% 219.39/170.80  							| (18)  ~ (all_0_0_0 = 0)
% 219.39/170.80  							| (267)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (doDivides0(all_0_2_2, xn) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.39/170.80  							|
% 219.39/170.80  								| Instantiating (267) with all_82_0_107, all_82_1_108, all_82_2_109, all_82_3_110 yields:
% 219.39/170.80  								| (268) doDivides0(all_0_2_2, xn) = all_82_0_107 & aNaturalNumber0(all_0_2_2) = all_82_2_109 & aNaturalNumber0(xp) = all_82_3_110 & aNaturalNumber0(xn) = all_82_1_108 & ( ~ (all_82_0_107 = 0) |  ~ (all_82_1_108 = 0) |  ~ (all_82_2_109 = 0) |  ~ (all_82_3_110 = 0))
% 219.39/170.80  								|
% 219.39/170.80  								| Applying alpha-rule on (268) yields:
% 219.39/170.80  								| (269) doDivides0(all_0_2_2, xn) = all_82_0_107
% 219.39/170.80  								| (270) aNaturalNumber0(xp) = all_82_3_110
% 219.39/170.80  								| (271) aNaturalNumber0(xn) = all_82_1_108
% 219.39/170.80  								| (272)  ~ (all_82_0_107 = 0) |  ~ (all_82_1_108 = 0) |  ~ (all_82_2_109 = 0) |  ~ (all_82_3_110 = 0)
% 219.39/170.80  								| (273) aNaturalNumber0(all_0_2_2) = all_82_2_109
% 219.39/170.80  								|
% 219.39/170.80  								+-Applying beta-rule and splitting (129), into two cases.
% 219.39/170.80  								|-Branch one:
% 219.39/170.80  								| (274) xr = sz00
% 219.39/170.80  								|
% 219.39/170.80  									| Equations (274) can reduce 100 to:
% 219.39/170.80  									| (197) $false
% 219.39/170.80  									|
% 219.39/170.80  									|-The branch is then unsatisfiable
% 219.39/170.80  								|-Branch two:
% 219.39/170.80  								| (100)  ~ (xr = sz00)
% 219.39/170.80  								| (277) xr = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 219.39/170.80  								|
% 219.39/170.80  									+-Applying beta-rule and splitting (130), into two cases.
% 219.39/170.80  									|-Branch one:
% 219.39/170.80  									| (278) xp = sz00
% 219.39/170.80  									|
% 219.39/170.80  										| Equations (278) can reduce 101 to:
% 219.39/170.80  										| (197) $false
% 219.39/170.80  										|
% 219.39/170.80  										|-The branch is then unsatisfiable
% 219.39/170.80  									|-Branch two:
% 219.39/170.80  									| (101)  ~ (xp = sz00)
% 219.39/170.80  									| (281) xp = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 219.39/170.80  									|
% 219.39/170.80  										+-Applying beta-rule and splitting (277), into two cases.
% 219.39/170.80  										|-Branch one:
% 219.39/170.80  										| (282) xr = sz10
% 219.39/170.80  										|
% 219.39/170.80  											| Equations (282) can reduce 98 to:
% 219.39/170.80  											| (197) $false
% 219.39/170.80  											|
% 219.39/170.80  											|-The branch is then unsatisfiable
% 219.39/170.80  										|-Branch two:
% 219.39/170.80  										| (98)  ~ (xr = sz10)
% 219.39/170.80  										| (285)  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 219.39/170.80  										|
% 219.39/170.80  											| Instantiating (285) with all_94_0_111 yields:
% 219.39/170.80  											| (286) isPrime0(all_94_0_111) = 0 & doDivides0(all_94_0_111, xr) = 0 & aNaturalNumber0(all_94_0_111) = 0
% 219.39/170.80  											|
% 219.39/170.80  											| Applying alpha-rule on (286) yields:
% 219.39/170.80  											| (287) isPrime0(all_94_0_111) = 0
% 219.39/170.80  											| (288) doDivides0(all_94_0_111, xr) = 0
% 219.39/170.80  											| (289) aNaturalNumber0(all_94_0_111) = 0
% 219.39/170.80  											|
% 219.39/170.80  											+-Applying beta-rule and splitting (281), into two cases.
% 219.39/170.80  											|-Branch one:
% 219.39/170.80  											| (290) xp = sz10
% 219.39/170.80  											|
% 219.39/170.80  												| Equations (290) can reduce 99 to:
% 219.39/170.80  												| (197) $false
% 219.39/170.80  												|
% 219.39/170.80  												|-The branch is then unsatisfiable
% 219.39/170.80  											|-Branch two:
% 219.39/170.80  											| (99)  ~ (xp = sz10)
% 219.39/170.80  											| (293)  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 219.39/170.80  											|
% 219.39/170.80  												| Instantiating (293) with all_99_0_112 yields:
% 219.39/170.80  												| (294) isPrime0(all_99_0_112) = 0 & doDivides0(all_99_0_112, xp) = 0 & aNaturalNumber0(all_99_0_112) = 0
% 219.39/170.81  												|
% 219.39/170.81  												| Applying alpha-rule on (294) yields:
% 219.39/170.81  												| (295) isPrime0(all_99_0_112) = 0
% 219.39/170.81  												| (296) doDivides0(all_99_0_112, xp) = 0
% 219.39/170.81  												| (297) aNaturalNumber0(all_99_0_112) = 0
% 219.39/170.81  												|
% 219.39/170.81  												| Using (295) and (32) yields:
% 219.39/170.81  												| (298)  ~ (all_99_0_112 = sz10)
% 219.39/170.81  												|
% 219.39/170.81  												| Using (295) and (15) yields:
% 219.39/170.81  												| (299)  ~ (all_99_0_112 = sz00)
% 219.39/170.81  												|
% 219.39/170.81  												| Using (287) and (32) yields:
% 219.39/170.81  												| (300)  ~ (all_94_0_111 = sz10)
% 219.39/170.81  												|
% 219.39/170.81  												| Using (287) and (15) yields:
% 219.39/170.81  												| (301)  ~ (all_94_0_111 = sz00)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (75) with xp, all_39_5_71, 0 and discharging atoms isPrime0(xp) = all_39_5_71, isPrime0(xp) = 0, yields:
% 219.39/170.81  												| (302) all_39_5_71 = 0
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (79) with xp, all_0_3_3, all_39_3_69, 0 and discharging atoms doDivides0(xp, all_0_3_3) = 0, yields:
% 219.39/170.81  												| (303) all_39_3_69 = 0 |  ~ (doDivides0(xp, all_0_3_3) = all_39_3_69)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (79) with xp, all_0_7_7, all_39_3_69, 0 and discharging atoms doDivides0(xp, all_0_7_7) = 0, yields:
% 219.39/170.81  												| (304) all_39_3_69 = 0 |  ~ (doDivides0(xp, all_0_7_7) = all_39_3_69)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (79) with xp, xn, all_39_1_67, 0 and discharging atoms doDivides0(xp, xn) = all_39_1_67, yields:
% 219.39/170.81  												| (305) all_39_1_67 = 0 |  ~ (doDivides0(xp, xn) = 0)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (79) with xp, xn, all_39_1_67, all_0_0_0 and discharging atoms doDivides0(xp, xn) = all_39_1_67, doDivides0(xp, xn) = all_0_0_0, yields:
% 219.39/170.81  												| (306) all_39_1_67 = all_0_0_0
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (49) with xn, xm, all_39_4_70, all_0_7_7 and discharging atoms sdtasdt0(xn, xm) = all_39_4_70, sdtasdt0(xn, xm) = all_0_7_7, yields:
% 219.39/170.81  												| (307) all_39_4_70 = all_0_7_7
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xr, all_82_2_109, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.81  												| (308) all_82_2_109 = 0 |  ~ (aNaturalNumber0(xr) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xp, all_82_2_109, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.81  												| (309) all_82_2_109 = 0 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xm, all_82_2_109, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.81  												| (310) all_82_2_109 = 0 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xn, all_82_2_109, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.81  												| (311) all_82_2_109 = 0 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz10, all_82_2_109, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.81  												| (312) all_82_2_109 = 0 |  ~ (aNaturalNumber0(sz10) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz00, all_82_2_109, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.81  												| (313) all_82_2_109 = 0 |  ~ (aNaturalNumber0(sz00) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_2_2, all_82_2_109, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_82_2_109, yields:
% 219.39/170.81  												| (314) all_82_2_109 = 0 |  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xr, all_67_2_97, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.81  												| (315) all_67_2_97 = 0 |  ~ (aNaturalNumber0(xr) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xp, all_67_2_97, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.81  												| (316) all_67_2_97 = 0 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xm, all_67_2_97, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.81  												| (317) all_67_2_97 = 0 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xn, all_67_2_97, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.81  												| (318) all_67_2_97 = 0 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz10, all_67_2_97, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.81  												| (319) all_67_2_97 = 0 |  ~ (aNaturalNumber0(sz10) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz00, all_67_2_97, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.81  												| (320) all_67_2_97 = 0 |  ~ (aNaturalNumber0(sz00) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_2_2, all_67_2_97, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_67_2_97, yields:
% 219.39/170.81  												| (321) all_67_2_97 = 0 |  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_2_2, all_67_2_97, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_2_2) = all_82_2_109, aNaturalNumber0(all_0_2_2) = all_67_2_97, yields:
% 219.39/170.81  												| (322) all_82_2_109 = all_67_2_97
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xr, all_20_0_22, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.81  												| (323) all_20_0_22 = 0 |  ~ (aNaturalNumber0(xr) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xp, all_20_0_22, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.81  												| (324) all_20_0_22 = 0 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xm, all_20_0_22, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.81  												| (325) all_20_0_22 = 0 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xn, all_20_0_22, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.81  												| (326) all_20_0_22 = 0 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz10, all_20_0_22, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.81  												| (327) all_20_0_22 = 0 |  ~ (aNaturalNumber0(sz10) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz00, all_20_0_22, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.81  												| (328) all_20_0_22 = 0 |  ~ (aNaturalNumber0(sz00) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_2_2, all_20_0_22, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_20_0_22, yields:
% 219.39/170.81  												| (329) all_20_0_22 = 0 |  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_2_2, all_20_0_22, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_2_2) = all_82_2_109, aNaturalNumber0(all_0_2_2) = all_20_0_22, yields:
% 219.39/170.81  												| (330) all_82_2_109 = all_20_0_22
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xr, all_72_2_101, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.81  												| (331) all_72_2_101 = 0 |  ~ (aNaturalNumber0(xr) = all_72_2_101)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xp, all_72_2_101, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.81  												| (332) all_72_2_101 = 0 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xm, all_72_2_101, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.81  												| (333) all_72_2_101 = 0 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz10, all_72_2_101, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.81  												| (334) all_72_2_101 = 0 |  ~ (aNaturalNumber0(sz10) = all_72_2_101)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz00, all_72_2_101, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.81  												| (335) all_72_2_101 = 0 |  ~ (aNaturalNumber0(sz00) = all_72_2_101)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_3_3, all_72_2_101, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_72_2_101, yields:
% 219.39/170.81  												| (336) all_72_2_101 = 0 |  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_3_3, all_72_2_101, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_3_3) = all_72_2_101, yields:
% 219.39/170.81  												| (337) all_82_2_109 = all_72_2_101 |  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_3_3, all_72_2_101, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_3_3) = all_72_2_101, yields:
% 219.39/170.81  												| (338) all_72_2_101 = all_67_2_97 |  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_3_3, all_72_2_101, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_3_3) = all_72_2_101, yields:
% 219.39/170.81  												| (339) all_72_2_101 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xr, all_62_2_94, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.81  												| (340) all_62_2_94 = 0 |  ~ (aNaturalNumber0(xr) = all_62_2_94)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xp, all_62_2_94, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.81  												| (341) all_62_2_94 = 0 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with xm, all_62_2_94, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.81  												| (342) all_62_2_94 = 0 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz10, all_62_2_94, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.81  												| (343) all_62_2_94 = 0 |  ~ (aNaturalNumber0(sz10) = all_62_2_94)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with sz00, all_62_2_94, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.81  												| (344) all_62_2_94 = 0 |  ~ (aNaturalNumber0(sz00) = all_62_2_94)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_3_3, all_62_2_94, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_62_2_94, yields:
% 219.39/170.81  												| (345) all_62_2_94 = 0 |  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 219.39/170.81  												|
% 219.39/170.81  												| Instantiating formula (28) with all_0_3_3, all_62_2_94, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_3_3) = all_62_2_94, yields:
% 219.39/170.81  												| (346) all_82_2_109 = all_62_2_94 |  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_62_2_94, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_3_3) = all_62_2_94, yields:
% 219.39/170.82  												| (347) all_67_2_97 = all_62_2_94 |  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_62_2_94, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_3_3) = all_62_2_94, yields:
% 219.39/170.82  												| (348) all_62_2_94 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_62_2_94, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_3_3) = all_72_2_101, aNaturalNumber0(all_0_3_3) = all_62_2_94, yields:
% 219.39/170.82  												| (349) all_72_2_101 = all_62_2_94
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xp, all_57_2_90, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.82  												| (350) all_57_2_90 = 0 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xm, all_57_2_90, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.82  												| (351) all_57_2_90 = 0 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz10, all_57_2_90, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.82  												| (352) all_57_2_90 = 0 |  ~ (aNaturalNumber0(sz10) = all_57_2_90)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz00, all_57_2_90, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.82  												| (353) all_57_2_90 = 0 |  ~ (aNaturalNumber0(sz00) = all_57_2_90)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_57_2_90, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_57_2_90, yields:
% 219.39/170.82  												| (354) all_57_2_90 = 0 |  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_57_2_90, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_3_3) = all_57_2_90, yields:
% 219.39/170.82  												| (355) all_82_2_109 = all_57_2_90 |  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_57_2_90, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_3_3) = all_57_2_90, yields:
% 219.39/170.82  												| (356) all_67_2_97 = all_57_2_90 |  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_57_2_90, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_3_3) = all_57_2_90, yields:
% 219.39/170.82  												| (357) all_57_2_90 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_57_2_90, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_3_3) = all_62_2_94, aNaturalNumber0(all_0_3_3) = all_57_2_90, yields:
% 219.39/170.82  												| (358) all_62_2_94 = all_57_2_90
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xr, all_22_2_27, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.82  												| (359) all_22_2_27 = 0 |  ~ (aNaturalNumber0(xr) = all_22_2_27)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xp, all_22_2_27, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.82  												| (360) all_22_2_27 = 0 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xm, all_22_2_27, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.82  												| (361) all_22_2_27 = 0 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz10, all_22_2_27, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.82  												| (362) all_22_2_27 = 0 |  ~ (aNaturalNumber0(sz10) = all_22_2_27)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz00, all_22_2_27, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.82  												| (363) all_22_2_27 = 0 |  ~ (aNaturalNumber0(sz00) = all_22_2_27)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_22_2_27, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_22_2_27, yields:
% 219.39/170.82  												| (364) all_22_2_27 = 0 |  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_22_2_27, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_3_3) = all_22_2_27, yields:
% 219.39/170.82  												| (365) all_82_2_109 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_22_2_27, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_3_3) = all_22_2_27, yields:
% 219.39/170.82  												| (366) all_67_2_97 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_22_2_27, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_3_3) = all_22_2_27, yields:
% 219.39/170.82  												| (367) all_22_2_27 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_22_2_27, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_3_3) = all_57_2_90, aNaturalNumber0(all_0_3_3) = all_22_2_27, yields:
% 219.39/170.82  												| (368) all_57_2_90 = all_22_2_27
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xr, all_20_2_24, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.82  												| (369) all_20_2_24 = 0 |  ~ (aNaturalNumber0(xr) = all_20_2_24)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xp, all_20_2_24, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.82  												| (370) all_20_2_24 = 0 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xm, all_20_2_24, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.82  												| (371) all_20_2_24 = 0 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz10, all_20_2_24, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.82  												| (372) all_20_2_24 = 0 |  ~ (aNaturalNumber0(sz10) = all_20_2_24)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz00, all_20_2_24, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.82  												| (373) all_20_2_24 = 0 |  ~ (aNaturalNumber0(sz00) = all_20_2_24)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_20_2_24, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_20_2_24, yields:
% 219.39/170.82  												| (374) all_20_2_24 = 0 |  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_20_2_24, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_3_3) = all_20_2_24, yields:
% 219.39/170.82  												| (375) all_82_2_109 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_20_2_24, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_3_3) = all_20_2_24, yields:
% 219.39/170.82  												| (376) all_67_2_97 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_20_2_24, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_3_3) = all_20_2_24, yields:
% 219.39/170.82  												| (377) all_20_0_22 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_3_3, all_20_2_24, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_3_3) = all_72_2_101, aNaturalNumber0(all_0_3_3) = all_20_2_24, yields:
% 219.39/170.82  												| (378) all_72_2_101 = all_20_2_24
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xr, all_77_2_105, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.82  												| (379) all_77_2_105 = 0 |  ~ (aNaturalNumber0(xr) = all_77_2_105)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xp, all_77_2_105, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.82  												| (380) all_77_2_105 = 0 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xm, all_77_2_105, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.82  												| (381) all_77_2_105 = 0 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xn, all_77_2_105, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.82  												| (382) all_77_2_105 = 0 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz10, all_77_2_105, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.82  												| (383) all_77_2_105 = 0 |  ~ (aNaturalNumber0(sz10) = all_77_2_105)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with sz00, all_77_2_105, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.82  												| (384) all_77_2_105 = 0 |  ~ (aNaturalNumber0(sz00) = all_77_2_105)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, 0 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (385) all_77_2_105 = 0 |  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (386) all_82_2_109 = all_77_2_105 |  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (387) all_77_2_105 = all_67_2_97 |  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (388) all_77_2_105 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (389) all_77_2_105 = all_72_2_101 |  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (390) all_77_2_105 = all_62_2_94 |  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (391) all_77_2_105 = all_57_2_90 |  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (392) all_77_2_105 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with all_0_7_7, all_77_2_105, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, yields:
% 219.39/170.82  												| (393) all_77_2_105 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_7_7) = all_20_2_24)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xr, all_47_2_83, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.82  												| (394) all_47_2_83 = 0 |  ~ (aNaturalNumber0(xr) = all_47_2_83)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xp, all_47_2_83, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.82  												| (395) all_47_2_83 = 0 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.82  												|
% 219.39/170.82  												| Instantiating formula (28) with xm, all_47_2_83, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.82  												| (396) all_47_2_83 = 0 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xn, all_47_2_83, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.83  												| (397) all_47_2_83 = 0 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz10, all_47_2_83, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.83  												| (398) all_47_2_83 = 0 |  ~ (aNaturalNumber0(sz10) = all_47_2_83)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz00, all_47_2_83, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.83  												| (399) all_47_2_83 = 0 |  ~ (aNaturalNumber0(sz00) = all_47_2_83)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, 0 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (400) all_47_2_83 = 0 |  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (401) all_82_2_109 = all_47_2_83 |  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (402) all_67_2_97 = all_47_2_83 |  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (403) all_47_2_83 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (404) all_72_2_101 = all_47_2_83 |  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (405) all_62_2_94 = all_47_2_83 |  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (406) all_57_2_90 = all_47_2_83 |  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (407) all_47_2_83 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_47_2_83, all_77_2_105 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, aNaturalNumber0(all_0_7_7) = all_47_2_83, yields:
% 219.39/170.83  												| (408) all_77_2_105 = all_47_2_83
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xr, all_16_0_16, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.83  												| (409) all_16_0_16 = 0 |  ~ (aNaturalNumber0(xr) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xp, all_16_0_16, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.83  												| (410) all_16_0_16 = 0 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xm, all_16_0_16, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.83  												| (411) all_16_0_16 = 0 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xn, all_16_0_16, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.83  												| (412) all_16_0_16 = 0 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz10, all_16_0_16, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.83  												| (413) all_16_0_16 = 0 |  ~ (aNaturalNumber0(sz10) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz00, all_16_0_16, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.83  												| (414) all_16_0_16 = 0 |  ~ (aNaturalNumber0(sz00) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, 0 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (415) all_16_0_16 = 0 |  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (416) all_82_2_109 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (417) all_67_2_97 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (418) all_20_0_22 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (419) all_72_2_101 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (420) all_62_2_94 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (421) all_57_2_90 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (422) all_22_2_27 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (423) all_20_2_24 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_7_7) = all_20_2_24)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_7_7, all_16_0_16, all_77_2_105 and discharging atoms aNaturalNumber0(all_0_7_7) = all_77_2_105, aNaturalNumber0(all_0_7_7) = all_16_0_16, yields:
% 219.39/170.83  												| (424) all_77_2_105 = all_16_0_16
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xr, all_24_0_28, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.83  												| (425) all_24_0_28 = 0 |  ~ (aNaturalNumber0(xr) = all_24_0_28)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xp, all_24_0_28, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.83  												| (426) all_24_0_28 = 0 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xm, all_24_0_28, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.83  												| (427) all_24_0_28 = 0 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xn, all_24_0_28, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.83  												| (428) all_24_0_28 = 0 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz10, all_24_0_28, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.83  												| (429) all_24_0_28 = 0 |  ~ (aNaturalNumber0(sz10) = all_24_0_28)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz00, all_24_0_28, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.83  												| (430) all_24_0_28 = 0 |  ~ (aNaturalNumber0(sz00) = all_24_0_28)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, 0 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (431) all_24_0_28 = 0 |  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (432) all_82_2_109 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_82_2_109)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (433) all_67_2_97 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_67_2_97)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (434) all_24_0_28 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_8_8) = all_20_0_22)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (435) all_72_2_101 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_72_2_101)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (436) all_62_2_94 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_62_2_94)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (437) all_57_2_90 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_57_2_90)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (438) all_24_0_28 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_8_8) = all_22_2_27)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (439) all_24_0_28 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_8_8) = all_20_2_24)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_77_2_105 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (440) all_77_2_105 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_77_2_105)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_47_2_83 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (441) all_47_2_83 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_8_8) = all_47_2_83)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_8_8, all_24_0_28, all_16_0_16 and discharging atoms aNaturalNumber0(all_0_8_8) = all_24_0_28, yields:
% 219.39/170.83  												| (442) all_24_0_28 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_8_8) = all_16_0_16)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xp, all_26_2_33, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.83  												| (443) all_26_2_33 = 0 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xm, all_26_2_33, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.83  												| (444) all_26_2_33 = 0 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with xn, all_26_2_33, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.83  												| (445) all_26_2_33 = 0 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz10, all_26_2_33, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.83  												| (446) all_26_2_33 = 0 |  ~ (aNaturalNumber0(sz10) = all_26_2_33)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with sz00, all_26_2_33, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.83  												| (447) all_26_2_33 = 0 |  ~ (aNaturalNumber0(sz00) = all_26_2_33)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.83  												| (448) all_26_2_33 = 0 |  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 219.39/170.83  												|
% 219.39/170.83  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (449) all_82_2_109 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (450) all_67_2_97 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (451) all_26_2_33 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (452) all_72_2_101 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (453) all_62_2_94 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (454) all_57_2_90 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (455) all_26_2_33 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (456) all_26_2_33 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_77_2_105 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (457) all_77_2_105 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_47_2_83 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (458) all_47_2_83 = all_26_2_33 |  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_16_0_16 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (459) all_26_2_33 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_26_2_33, all_24_0_28 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, yields:
% 219.39/170.84  												| (460) all_26_2_33 = all_24_0_28 |  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xr, all_24_2_30, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.84  												| (461) all_24_2_30 = 0 |  ~ (aNaturalNumber0(xr) = all_24_2_30)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xp, all_24_2_30, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.84  												| (462) all_24_2_30 = 0 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xm, all_24_2_30, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.84  												| (463) all_24_2_30 = 0 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xn, all_24_2_30, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.84  												| (464) all_24_2_30 = 0 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with sz10, all_24_2_30, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.84  												| (465) all_24_2_30 = 0 |  ~ (aNaturalNumber0(sz10) = all_24_2_30)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with sz00, all_24_2_30, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.84  												| (466) all_24_2_30 = 0 |  ~ (aNaturalNumber0(sz00) = all_24_2_30)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (467) all_24_2_30 = 0 |  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (468) all_82_2_109 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (469) all_67_2_97 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (470) all_24_2_30 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (471) all_72_2_101 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (472) all_62_2_94 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (473) all_57_2_90 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (474) all_24_2_30 = all_22_2_27 |  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (475) all_24_2_30 = all_20_2_24 |  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_77_2_105 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (476) all_77_2_105 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_47_2_83 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (477) all_47_2_83 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_16_0_16 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (478) all_24_2_30 = all_16_0_16 |  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_24_0_28 and discharging atoms aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (479) all_24_0_28 = all_24_2_30 |  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_24_2_30, all_26_2_33 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, aNaturalNumber0(all_0_9_9) = all_24_2_30, yields:
% 219.39/170.84  												| (480) all_26_2_33 = all_24_2_30
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xr, all_12_0_10, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 219.39/170.84  												| (481) all_12_0_10 = 0 |  ~ (aNaturalNumber0(xr) = all_12_0_10)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xp, all_12_0_10, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 219.39/170.84  												| (482) all_12_0_10 = 0 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xm, all_12_0_10, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.84  												| (483) all_12_0_10 = 0 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xn, all_12_0_10, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.84  												| (484) all_12_0_10 = 0 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with sz10, all_12_0_10, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.84  												| (485) all_12_0_10 = 0 |  ~ (aNaturalNumber0(sz10) = all_12_0_10)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with sz00, all_12_0_10, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.84  												| (486) all_12_0_10 = 0 |  ~ (aNaturalNumber0(sz00) = all_12_0_10)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (487) all_12_0_10 = 0 |  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_82_2_109 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (488) all_82_2_109 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_67_2_97 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (489) all_67_2_97 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (490) all_20_0_22 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_72_2_101 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (491) all_72_2_101 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_62_2_94 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (492) all_62_2_94 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_57_2_90 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (493) all_57_2_90 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_22_2_27 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (494) all_22_2_27 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (495) all_20_2_24 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_77_2_105 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (496) all_77_2_105 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_47_2_83 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (497) all_47_2_83 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_16_0_16 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (498) all_16_0_16 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_24_0_28 and discharging atoms aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (499) all_24_0_28 = all_12_0_10 |  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with all_0_9_9, all_12_0_10, all_26_2_33 and discharging atoms aNaturalNumber0(all_0_9_9) = all_26_2_33, aNaturalNumber0(all_0_9_9) = all_12_0_10, yields:
% 219.39/170.84  												| (500) all_26_2_33 = all_12_0_10
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xk, all_52_2_87, 0 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.84  												| (501) all_52_2_87 = 0 |  ~ (aNaturalNumber0(xk) = 0)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xm, all_52_2_87, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 219.39/170.84  												| (502) all_52_2_87 = 0 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xn, all_52_2_87, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.84  												| (503) all_52_2_87 = 0 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xk, all_52_2_87, all_82_2_109 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.84  												| (504) all_82_2_109 = all_52_2_87 |  ~ (aNaturalNumber0(xk) = all_82_2_109)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xk, all_52_2_87, all_67_2_97 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.84  												| (505) all_67_2_97 = all_52_2_87 |  ~ (aNaturalNumber0(xk) = all_67_2_97)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xk, all_52_2_87, all_20_0_22 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.84  												| (506) all_52_2_87 = all_20_0_22 |  ~ (aNaturalNumber0(xk) = all_20_0_22)
% 219.39/170.84  												|
% 219.39/170.84  												| Instantiating formula (28) with xk, all_52_2_87, all_72_2_101 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (507) all_72_2_101 = all_52_2_87 |  ~ (aNaturalNumber0(xk) = all_72_2_101)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_62_2_94 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (508) all_62_2_94 = all_52_2_87 |  ~ (aNaturalNumber0(xk) = all_62_2_94)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_57_2_90 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (509) all_57_2_90 = all_52_2_87 |  ~ (aNaturalNumber0(xk) = all_57_2_90)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_22_2_27 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (510) all_52_2_87 = all_22_2_27 |  ~ (aNaturalNumber0(xk) = all_22_2_27)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_20_2_24 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (511) all_52_2_87 = all_20_2_24 |  ~ (aNaturalNumber0(xk) = all_20_2_24)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_77_2_105 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (512) all_77_2_105 = all_52_2_87 |  ~ (aNaturalNumber0(xk) = all_77_2_105)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_47_2_83 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (513) all_52_2_87 = all_47_2_83 |  ~ (aNaturalNumber0(xk) = all_47_2_83)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_16_0_16 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (514) all_52_2_87 = all_16_0_16 |  ~ (aNaturalNumber0(xk) = all_16_0_16)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_24_0_28 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (515) all_52_2_87 = all_24_0_28 |  ~ (aNaturalNumber0(xk) = all_24_0_28)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_26_2_33 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (516) all_52_2_87 = all_26_2_33 |  ~ (aNaturalNumber0(xk) = all_26_2_33)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_24_2_30 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (517) all_52_2_87 = all_24_2_30 |  ~ (aNaturalNumber0(xk) = all_24_2_30)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xk, all_52_2_87, all_12_0_10 and discharging atoms aNaturalNumber0(xk) = all_52_2_87, yields:
% 219.39/170.85  												| (518) all_52_2_87 = all_12_0_10 |  ~ (aNaturalNumber0(xk) = all_12_0_10)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (519) all_82_2_109 = all_82_3_110 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (520) all_82_3_110 = all_67_2_97 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (521) all_82_3_110 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (522) all_82_3_110 = all_72_2_101 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (523) all_82_3_110 = all_62_2_94 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (524) all_82_3_110 = all_57_2_90 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (525) all_82_3_110 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (526) all_82_3_110 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (527) all_82_3_110 = all_77_2_105 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (528) all_82_3_110 = all_47_2_83 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (529) all_82_3_110 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (530) all_82_3_110 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (531) all_82_3_110 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (532) all_82_3_110 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_82_3_110, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, yields:
% 219.39/170.85  												| (533) all_82_3_110 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (534) all_82_2_109 = all_77_3_106 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (535) all_77_3_106 = all_67_2_97 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (536) all_77_3_106 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (537) all_77_3_106 = all_72_2_101 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (538) all_77_3_106 = all_62_2_94 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (539) all_77_3_106 = all_57_2_90 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (540) all_77_3_106 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (541) all_77_3_106 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (542) all_77_2_105 = all_77_3_106 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (543) all_77_3_106 = all_47_2_83 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (544) all_77_3_106 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (545) all_77_3_106 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (546) all_77_3_106 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (547) all_77_3_106 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (548) all_77_3_106 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_77_3_106, all_82_3_110 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, aNaturalNumber0(xp) = all_77_3_106, yields:
% 219.39/170.85  												| (549) all_82_3_110 = all_77_3_106
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (550) all_82_2_109 = all_72_3_102 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (551) all_72_3_102 = all_67_2_97 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (552) all_72_3_102 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (553) all_72_2_101 = all_72_3_102 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (554) all_72_3_102 = all_62_2_94 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (555) all_72_3_102 = all_57_2_90 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (556) all_72_3_102 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (557) all_72_3_102 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (558) all_77_2_105 = all_72_3_102 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (559) all_72_3_102 = all_47_2_83 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (560) all_72_3_102 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (561) all_72_3_102 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (562) all_72_3_102 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (563) all_72_3_102 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (564) all_72_3_102 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_72_3_102, all_77_3_106 and discharging atoms aNaturalNumber0(xp) = all_77_3_106, aNaturalNumber0(xp) = all_72_3_102, yields:
% 219.39/170.85  												| (565) all_77_3_106 = all_72_3_102
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (566) all_82_2_109 = all_67_3_98 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (567) all_67_2_97 = all_67_3_98 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (568) all_67_3_98 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (569) all_72_2_101 = all_67_3_98 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (570) all_67_3_98 = all_62_2_94 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (571) all_67_3_98 = all_57_2_90 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (572) all_67_3_98 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.85  												| (573) all_67_3_98 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.85  												|
% 219.39/170.85  												| Instantiating formula (28) with xp, all_67_3_98, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (574) all_77_2_105 = all_67_3_98 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (575) all_67_3_98 = all_47_2_83 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (576) all_67_3_98 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (577) all_67_3_98 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (578) all_67_3_98 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (579) all_67_3_98 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (580) all_67_3_98 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_67_3_98, all_72_3_102 and discharging atoms aNaturalNumber0(xp) = all_72_3_102, aNaturalNumber0(xp) = all_67_3_98, yields:
% 219.39/170.86  												| (581) all_72_3_102 = all_67_3_98
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (582) all_82_2_109 = all_57_3_91 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (583) all_67_2_97 = all_57_3_91 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (584) all_57_3_91 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (585) all_72_2_101 = all_57_3_91 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (586) all_62_2_94 = all_57_3_91 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (587) all_57_2_90 = all_57_3_91 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (588) all_57_3_91 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (589) all_57_3_91 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (590) all_77_2_105 = all_57_3_91 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (591) all_57_3_91 = all_47_2_83 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (592) all_57_3_91 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (593) all_57_3_91 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (594) all_57_3_91 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (595) all_57_3_91 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_57_3_91, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, yields:
% 219.39/170.86  												| (596) all_57_3_91 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (597) all_82_2_109 = all_52_1_86 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (598) all_67_2_97 = all_52_1_86 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (599) all_52_1_86 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (600) all_72_2_101 = all_52_1_86 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (601) all_62_2_94 = all_52_1_86 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (602) all_57_2_90 = all_52_1_86 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (603) all_52_1_86 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (604) all_52_1_86 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (605) all_77_2_105 = all_52_1_86 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (606) all_52_1_86 = all_47_2_83 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (607) all_52_1_86 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (608) all_52_1_86 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (609) all_52_1_86 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (610) all_52_1_86 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (611) all_52_1_86 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_52_1_86, all_57_3_91 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, aNaturalNumber0(xp) = all_52_1_86, yields:
% 219.39/170.86  												| (612) all_57_3_91 = all_52_1_86
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (613) all_82_2_109 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (614) all_67_2_97 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (615) all_47_3_84 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (616) all_72_2_101 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (617) all_62_2_94 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (618) all_57_2_90 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (619) all_47_3_84 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (620) all_47_3_84 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (621) all_77_2_105 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (622) all_47_2_83 = all_47_3_84 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (623) all_47_3_84 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (624) all_47_3_84 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (625) all_47_3_84 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (626) all_47_3_84 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (627) all_47_3_84 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_47_3_84, all_67_3_98 and discharging atoms aNaturalNumber0(xp) = all_67_3_98, aNaturalNumber0(xp) = all_47_3_84, yields:
% 219.39/170.86  												| (628) all_67_3_98 = all_47_3_84
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, 0 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, aNaturalNumber0(xp) = 0, yields:
% 219.39/170.86  												| (629) all_39_6_72 = 0
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (630) all_82_2_109 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (631) all_67_2_97 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (632) all_39_6_72 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (633) all_72_2_101 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (634) all_62_2_94 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (635) all_57_2_90 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (636) all_39_6_72 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (637) all_39_6_72 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (638) all_77_2_105 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (639) all_47_2_83 = all_39_6_72 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (640) all_39_6_72 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.86  												| (641) all_39_6_72 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.86  												|
% 219.39/170.86  												| Instantiating formula (28) with xp, all_39_6_72, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.87  												| (642) all_39_6_72 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_39_6_72, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.87  												| (643) all_39_6_72 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_39_6_72, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, yields:
% 219.39/170.87  												| (644) all_39_6_72 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (645) all_82_2_109 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (646) all_67_2_97 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (647) all_37_2_63 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (648) all_72_2_101 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (649) all_62_2_94 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (650) all_57_2_90 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (651) all_37_2_63 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (652) all_37_2_63 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (653) all_77_2_105 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (654) all_47_2_83 = all_37_2_63 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (655) all_37_2_63 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (656) all_37_2_63 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (657) all_37_2_63 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (658) all_37_2_63 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (659) all_37_2_63 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_52_1_86 and discharging atoms aNaturalNumber0(xp) = all_52_1_86, aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (660) all_52_1_86 = all_37_2_63
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_47_3_84 and discharging atoms aNaturalNumber0(xp) = all_47_3_84, aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (661) all_47_3_84 = all_37_2_63
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_37_2_63, all_39_6_72 and discharging atoms aNaturalNumber0(xp) = all_39_6_72, aNaturalNumber0(xp) = all_37_2_63, yields:
% 219.39/170.87  												| (662) all_39_6_72 = all_37_2_63
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (663) all_82_2_109 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (664) all_67_2_97 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (665) all_26_1_32 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (666) all_72_2_101 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (667) all_62_2_94 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (668) all_57_2_90 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (669) all_26_1_32 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (670) all_26_1_32 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (671) all_77_2_105 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (672) all_47_2_83 = all_26_1_32 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (673) all_26_1_32 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (674) all_26_1_32 = all_24_0_28 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (675) all_26_1_32 = all_26_2_33 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (676) all_26_1_32 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (677) all_26_1_32 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_26_1_32, all_82_3_110 and discharging atoms aNaturalNumber0(xp) = all_82_3_110, aNaturalNumber0(xp) = all_26_1_32, yields:
% 219.39/170.87  												| (678) all_82_3_110 = all_26_1_32
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_82_2_109 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (679) all_82_2_109 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_67_2_97 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (680) all_67_2_97 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_20_0_22 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (681) all_24_1_29 = all_20_0_22 |  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_72_2_101 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (682) all_72_2_101 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_62_2_94 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (683) all_62_2_94 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_57_2_90 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (684) all_57_2_90 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_22_2_27 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (685) all_24_1_29 = all_22_2_27 |  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_20_2_24 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (686) all_24_1_29 = all_20_2_24 |  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_77_2_105 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (687) all_77_2_105 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_47_2_83 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (688) all_47_2_83 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_16_0_16 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (689) all_24_1_29 = all_16_0_16 |  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_24_0_28 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (690) all_24_0_28 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_26_2_33 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (691) all_26_2_33 = all_24_1_29 |  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_24_2_30 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (692) all_24_1_29 = all_24_2_30 |  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_12_0_10 and discharging atoms aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (693) all_24_1_29 = all_12_0_10 |  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xp, all_24_1_29, all_57_3_91 and discharging atoms aNaturalNumber0(xp) = all_57_3_91, aNaturalNumber0(xp) = all_24_1_29, yields:
% 219.39/170.87  												| (694) all_57_3_91 = all_24_1_29
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xn, all_72_1_100, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.87  												| (695) all_72_1_100 = 0 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with sz10, all_72_1_100, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.87  												| (696) all_72_1_100 = 0 |  ~ (aNaturalNumber0(sz10) = all_72_1_100)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (697) all_82_2_109 = all_72_1_100 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (698) all_72_1_100 = all_67_2_97 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (699) all_72_1_100 = all_20_0_22 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (700) all_72_1_100 = all_72_2_101 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (701) all_72_1_100 = all_62_2_94 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (702) all_72_1_100 = all_57_2_90 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (703) all_72_1_100 = all_22_2_27 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (704) all_72_1_100 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (705) all_77_2_105 = all_72_1_100 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (706) all_72_1_100 = all_47_2_83 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (707) all_72_1_100 = all_16_0_16 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (708) all_72_1_100 = all_24_0_28 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.87  												|
% 219.39/170.87  												| Instantiating formula (28) with xm, all_72_1_100, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.87  												| (709) all_72_1_100 = all_26_2_33 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_72_1_100, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.88  												| (710) all_72_1_100 = all_24_2_30 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_72_1_100, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.88  												| (711) all_72_1_100 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_72_1_100, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, yields:
% 219.39/170.88  												| (712) all_72_1_100 = all_52_2_87 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xn, all_67_1_96, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.88  												| (713) all_67_1_96 = 0 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz10, all_67_1_96, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.88  												| (714) all_67_1_96 = 0 |  ~ (aNaturalNumber0(sz10) = all_67_1_96)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz00, all_67_1_96, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.88  												| (715) all_67_1_96 = 0 |  ~ (aNaturalNumber0(sz00) = all_67_1_96)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (716) all_82_2_109 = all_67_1_96 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (717) all_67_1_96 = all_67_2_97 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (718) all_67_1_96 = all_20_0_22 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (719) all_72_2_101 = all_67_1_96 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (720) all_67_1_96 = all_62_2_94 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (721) all_67_1_96 = all_57_2_90 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (722) all_67_1_96 = all_22_2_27 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (723) all_67_1_96 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (724) all_77_2_105 = all_67_1_96 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (725) all_67_1_96 = all_47_2_83 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (726) all_67_1_96 = all_16_0_16 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (727) all_67_1_96 = all_24_0_28 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (728) all_67_1_96 = all_26_2_33 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (729) all_67_1_96 = all_24_2_30 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (730) all_67_1_96 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (731) all_67_1_96 = all_52_2_87 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_67_1_96, all_72_1_100 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, aNaturalNumber0(xm) = all_67_1_96, yields:
% 219.39/170.88  												| (732) all_72_1_100 = all_67_1_96
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xn, all_47_1_82, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.88  												| (733) all_47_1_82 = 0 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz10, all_47_1_82, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.88  												| (734) all_47_1_82 = 0 |  ~ (aNaturalNumber0(sz10) = all_47_1_82)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz00, all_47_1_82, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.88  												| (735) all_47_1_82 = 0 |  ~ (aNaturalNumber0(sz00) = all_47_1_82)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (736) all_82_2_109 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (737) all_67_2_97 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (738) all_47_1_82 = all_20_0_22 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (739) all_72_2_101 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (740) all_62_2_94 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (741) all_57_2_90 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (742) all_47_1_82 = all_22_2_27 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (743) all_47_1_82 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (744) all_77_2_105 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (745) all_47_1_82 = all_47_2_83 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (746) all_47_1_82 = all_24_0_28 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (747) all_47_1_82 = all_26_2_33 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (748) all_47_1_82 = all_24_2_30 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (749) all_47_1_82 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_47_1_82, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, yields:
% 219.39/170.88  												| (750) all_52_2_87 = all_47_1_82 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xn, all_39_7_73, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.88  												| (751) all_39_7_73 = 0 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz10, all_39_7_73, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.88  												| (752) all_39_7_73 = 0 |  ~ (aNaturalNumber0(sz10) = all_39_7_73)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz00, all_39_7_73, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.88  												| (753) all_39_7_73 = 0 |  ~ (aNaturalNumber0(sz00) = all_39_7_73)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (754) all_82_2_109 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (755) all_67_2_97 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (756) all_39_7_73 = all_20_0_22 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (757) all_72_2_101 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (758) all_62_2_94 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (759) all_57_2_90 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (760) all_39_7_73 = all_22_2_27 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (761) all_39_7_73 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (762) all_77_2_105 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (763) all_47_2_83 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (764) all_39_7_73 = all_16_0_16 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (765) all_39_7_73 = all_24_0_28 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (766) all_39_7_73 = all_26_2_33 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (767) all_39_7_73 = all_24_2_30 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (768) all_39_7_73 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_39_7_73, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, yields:
% 219.39/170.88  												| (769) all_52_2_87 = all_39_7_73 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xn, all_37_3_64, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.88  												| (770) all_37_3_64 = 0 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz10, all_37_3_64, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.88  												| (771) all_37_3_64 = 0 |  ~ (aNaturalNumber0(sz10) = all_37_3_64)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with sz00, all_37_3_64, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.88  												| (772) all_37_3_64 = 0 |  ~ (aNaturalNumber0(sz00) = all_37_3_64)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (773) all_82_2_109 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (774) all_67_2_97 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (775) all_37_3_64 = all_20_0_22 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (776) all_72_2_101 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (777) all_62_2_94 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (778) all_57_2_90 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (779) all_37_3_64 = all_22_2_27 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.88  												|
% 219.39/170.88  												| Instantiating formula (28) with xm, all_37_3_64, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.88  												| (780) all_37_3_64 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (781) all_77_2_105 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (782) all_47_2_83 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (783) all_37_3_64 = all_16_0_16 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (784) all_37_3_64 = all_24_0_28 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (785) all_37_3_64 = all_26_2_33 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (786) all_37_3_64 = all_24_2_30 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (787) all_37_3_64 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (788) all_52_2_87 = all_37_3_64 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_67_1_96 and discharging atoms aNaturalNumber0(xm) = all_67_1_96, aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (789) all_67_1_96 = all_37_3_64
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_47_1_82 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (790) all_47_1_82 = all_37_3_64
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_37_3_64, all_39_7_73 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, aNaturalNumber0(xm) = all_37_3_64, yields:
% 219.39/170.89  												| (791) all_39_7_73 = all_37_3_64
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xn, all_22_1_26, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.89  												| (792) all_22_1_26 = 0 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with sz10, all_22_1_26, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.89  												| (793) all_22_1_26 = 0 |  ~ (aNaturalNumber0(sz10) = all_22_1_26)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with sz00, all_22_1_26, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.39/170.89  												| (794) all_22_1_26 = 0 |  ~ (aNaturalNumber0(sz00) = all_22_1_26)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (795) all_82_2_109 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (796) all_67_2_97 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (797) all_22_1_26 = all_20_0_22 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (798) all_72_2_101 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (799) all_62_2_94 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (800) all_57_2_90 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (801) all_22_1_26 = all_22_2_27 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (802) all_22_1_26 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (803) all_77_2_105 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (804) all_47_2_83 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (805) all_22_1_26 = all_16_0_16 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (806) all_24_0_28 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (807) all_26_2_33 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (808) all_22_1_26 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (809) all_52_2_87 = all_22_1_26 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xm, all_22_1_26, all_72_1_100 and discharging atoms aNaturalNumber0(xm) = all_72_1_100, aNaturalNumber0(xm) = all_22_1_26, yields:
% 219.39/170.89  												| (810) all_72_1_100 = all_22_1_26
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with xn, all_20_1_23, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.39/170.89  												| (811) all_20_1_23 = 0 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.39/170.89  												|
% 219.39/170.89  												| Instantiating formula (28) with sz10, all_20_1_23, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.39/170.89  												| (812) all_20_1_23 = 0 |  ~ (aNaturalNumber0(sz10) = all_20_1_23)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with sz00, all_20_1_23, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.85/170.89  												| (813) all_20_1_23 = 0 |  ~ (aNaturalNumber0(sz00) = all_20_1_23)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (814) all_82_2_109 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (815) all_67_2_97 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (816) all_20_0_22 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (817) all_72_2_101 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (818) all_62_2_94 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (819) all_57_2_90 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (820) all_22_2_27 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (821) all_20_1_23 = all_20_2_24 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (822) all_77_2_105 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (823) all_24_0_28 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (824) all_24_2_30 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (825) all_20_1_23 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (826) all_52_2_87 = all_20_1_23 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_20_1_23, all_47_1_82 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, aNaturalNumber0(xm) = all_20_1_23, yields:
% 219.85/170.89  												| (827) all_47_1_82 = all_20_1_23
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xn, all_18_1_20, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.85/170.89  												| (828) all_18_1_20 = 0 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with sz10, all_18_1_20, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.85/170.89  												| (829) all_18_1_20 = 0 |  ~ (aNaturalNumber0(sz10) = all_18_1_20)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with sz00, all_18_1_20, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.85/170.89  												| (830) all_18_1_20 = 0 |  ~ (aNaturalNumber0(sz00) = all_18_1_20)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (831) all_82_2_109 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (832) all_67_2_97 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (833) all_20_0_22 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (834) all_72_2_101 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (835) all_62_2_94 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (836) all_57_2_90 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (837) all_22_2_27 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (838) all_20_2_24 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (839) all_77_2_105 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (840) all_47_2_83 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (841) all_18_1_20 = all_16_0_16 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (842) all_24_0_28 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (843) all_26_2_33 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (844) all_24_2_30 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (845) all_18_1_20 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (846) all_52_2_87 = all_18_1_20 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_18_1_20, all_39_7_73 and discharging atoms aNaturalNumber0(xm) = all_39_7_73, aNaturalNumber0(xm) = all_18_1_20, yields:
% 219.85/170.89  												| (847) all_39_7_73 = all_18_1_20
% 219.85/170.89  												|
% 219.85/170.89  												| Instantiating formula (28) with xm, all_16_1_17, 0 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, aNaturalNumber0(xm) = 0, yields:
% 219.85/170.90  												| (848) all_16_1_17 = 0
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xn, all_16_1_17, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.85/170.90  												| (849) all_16_1_17 = 0 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with sz10, all_16_1_17, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.85/170.90  												| (850) all_16_1_17 = 0 |  ~ (aNaturalNumber0(sz10) = all_16_1_17)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with sz00, all_16_1_17, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.85/170.90  												| (851) all_16_1_17 = 0 |  ~ (aNaturalNumber0(sz00) = all_16_1_17)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (852) all_82_2_109 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (853) all_67_2_97 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (854) all_20_0_22 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (855) all_72_2_101 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (856) all_62_2_94 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (857) all_57_2_90 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (858) all_22_2_27 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (859) all_20_2_24 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (860) all_77_2_105 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (861) all_47_2_83 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (862) all_16_0_16 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (863) all_24_0_28 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (864) all_26_2_33 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.85/170.90  												|
% 219.85/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.85/170.90  												| (865) all_24_2_30 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.88/170.90  												| (866) all_16_1_17 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_16_1_17, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, yields:
% 219.88/170.90  												| (867) all_52_2_87 = all_16_1_17 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_14_1_14, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.88/170.90  												| (868) all_14_1_14 = 0 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with sz10, all_14_1_14, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.88/170.90  												| (869) all_14_1_14 = 0 |  ~ (aNaturalNumber0(sz10) = all_14_1_14)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with sz00, all_14_1_14, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.88/170.90  												| (870) all_14_1_14 = 0 |  ~ (aNaturalNumber0(sz00) = all_14_1_14)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (871) all_82_2_109 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (872) all_67_2_97 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (873) all_20_0_22 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (874) all_72_2_101 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (875) all_62_2_94 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (876) all_57_2_90 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (877) all_22_2_27 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (878) all_20_2_24 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (879) all_77_2_105 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (880) all_47_2_83 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (881) all_16_0_16 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (882) all_24_0_28 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (883) all_26_2_33 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (884) all_24_2_30 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (885) all_14_1_14 = all_12_0_10 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_52_2_87 and discharging atoms aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (886) all_52_2_87 = all_14_1_14 |  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_47_1_82 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (887) all_47_1_82 = all_14_1_14
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_14_1_14, all_16_1_17 and discharging atoms aNaturalNumber0(xm) = all_16_1_17, aNaturalNumber0(xm) = all_14_1_14, yields:
% 219.88/170.90  												| (888) all_16_1_17 = all_14_1_14
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_12_1_11, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 219.88/170.90  												| (889) all_12_1_11 = 0 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with sz10, all_12_1_11, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.88/170.90  												| (890) all_12_1_11 = 0 |  ~ (aNaturalNumber0(sz10) = all_12_1_11)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with sz00, all_12_1_11, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.88/170.90  												| (891) all_12_1_11 = 0 |  ~ (aNaturalNumber0(sz00) = all_12_1_11)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_82_2_109 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (892) all_82_2_109 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_67_2_97 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (893) all_67_2_97 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_20_0_22 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (894) all_20_0_22 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_72_2_101 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (895) all_72_2_101 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_62_2_94 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (896) all_62_2_94 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_57_2_90 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (897) all_57_2_90 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_22_2_27 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (898) all_22_2_27 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_20_2_24 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (899) all_20_2_24 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_77_2_105 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (900) all_77_2_105 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_47_2_83 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (901) all_47_2_83 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_16_0_16 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (902) all_16_0_16 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_24_0_28 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (903) all_24_0_28 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_26_2_33 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (904) all_26_2_33 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_24_2_30 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (905) all_24_2_30 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_12_0_10 and discharging atoms aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (906) all_12_0_10 = all_12_1_11 |  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xm, all_12_1_11, all_47_1_82 and discharging atoms aNaturalNumber0(xm) = all_47_1_82, aNaturalNumber0(xm) = all_12_1_11, yields:
% 219.88/170.90  												| (907) all_47_1_82 = all_12_1_11
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with sz10, all_82_1_108, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.88/170.90  												| (908) all_82_1_108 = 0 |  ~ (aNaturalNumber0(sz10) = all_82_1_108)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with sz00, all_82_1_108, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.88/170.90  												| (909) all_82_1_108 = 0 |  ~ (aNaturalNumber0(sz00) = all_82_1_108)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (910) all_82_1_108 = all_82_2_109 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (911) all_82_1_108 = all_67_2_97 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (912) all_82_1_108 = all_20_0_22 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (913) all_82_1_108 = all_77_2_105 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (914) all_82_1_108 = all_47_2_83 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (915) all_82_1_108 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (916) all_82_1_108 = all_24_0_28 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (917) all_82_1_108 = all_26_2_33 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.88/170.90  												|
% 219.88/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.88/170.90  												| (918) all_82_1_108 = all_24_2_30 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.90  												|
% 219.91/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.90  												| (919) all_82_1_108 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.90  												|
% 219.91/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.90  												| (920) all_82_1_108 = all_52_2_87 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.90  												|
% 219.91/170.90  												| Instantiating formula (28) with xn, all_82_1_108, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (921) all_82_1_108 = all_72_1_100 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (922) all_82_1_108 = all_67_1_96 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (923) all_82_1_108 = all_47_1_82 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (924) all_82_1_108 = all_39_7_73 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (925) all_82_1_108 = all_37_3_64 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (926) all_82_1_108 = all_22_1_26 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (927) all_82_1_108 = all_20_1_23 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (928) all_82_1_108 = all_18_1_20 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (929) all_82_1_108 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (930) all_82_1_108 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_82_1_108, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, yields:
% 219.91/170.91  												| (931) all_82_1_108 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with sz10, all_77_1_104, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.91  												| (932) all_77_1_104 = 0 |  ~ (aNaturalNumber0(sz10) = all_77_1_104)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with sz00, all_77_1_104, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.91  												| (933) all_77_1_104 = 0 |  ~ (aNaturalNumber0(sz00) = all_77_1_104)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (934) all_82_2_109 = all_77_1_104 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (935) all_77_1_104 = all_67_2_97 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (936) all_77_1_104 = all_20_0_22 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (937) all_77_1_104 = all_77_2_105 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (938) all_77_1_104 = all_47_2_83 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (939) all_77_1_104 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (940) all_77_1_104 = all_24_0_28 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (941) all_77_1_104 = all_26_2_33 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (942) all_77_1_104 = all_24_2_30 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (943) all_77_1_104 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (944) all_77_1_104 = all_52_2_87 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (945) all_77_1_104 = all_72_1_100 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (946) all_77_1_104 = all_67_1_96 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (947) all_77_1_104 = all_39_7_73 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (948) all_77_1_104 = all_37_3_64 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (949) all_77_1_104 = all_22_1_26 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (950) all_77_1_104 = all_20_1_23 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (951) all_77_1_104 = all_18_1_20 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (952) all_77_1_104 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (953) all_77_1_104 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (954) all_77_1_104 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_77_1_104, all_82_1_108 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, aNaturalNumber0(xn) = all_77_1_104, yields:
% 219.91/170.91  												| (955) all_82_1_108 = all_77_1_104
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with sz10, all_62_1_93, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.91  												| (956) all_62_1_93 = 0 |  ~ (aNaturalNumber0(sz10) = all_62_1_93)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with sz00, all_62_1_93, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.91  												| (957) all_62_1_93 = 0 |  ~ (aNaturalNumber0(sz00) = all_62_1_93)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (958) all_82_2_109 = all_62_1_93 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (959) all_67_2_97 = all_62_1_93 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (960) all_62_1_93 = all_20_0_22 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (961) all_77_2_105 = all_62_1_93 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (962) all_62_1_93 = all_47_2_83 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (963) all_62_1_93 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (964) all_62_1_93 = all_24_0_28 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (965) all_62_1_93 = all_26_2_33 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (966) all_62_1_93 = all_24_2_30 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (967) all_62_1_93 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (968) all_62_1_93 = all_52_2_87 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (969) all_72_1_100 = all_62_1_93 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (970) all_67_1_96 = all_62_1_93 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (971) all_62_1_93 = all_47_1_82 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (972) all_62_1_93 = all_39_7_73 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (973) all_62_1_93 = all_37_3_64 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (974) all_62_1_93 = all_22_1_26 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (975) all_62_1_93 = all_20_1_23 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (976) all_62_1_93 = all_18_1_20 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (977) all_62_1_93 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (978) all_62_1_93 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_62_1_93, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, yields:
% 219.91/170.91  												| (979) all_62_1_93 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, 0 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, aNaturalNumber0(xn) = 0, yields:
% 219.91/170.91  												| (980) all_57_1_89 = 0
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with sz10, all_57_1_89, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.91  												| (981) all_57_1_89 = 0 |  ~ (aNaturalNumber0(sz10) = all_57_1_89)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with sz00, all_57_1_89, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.91  												| (982) all_57_1_89 = 0 |  ~ (aNaturalNumber0(sz00) = all_57_1_89)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (983) all_82_2_109 = all_57_1_89 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (984) all_67_2_97 = all_57_1_89 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (985) all_57_1_89 = all_20_0_22 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (986) all_77_2_105 = all_57_1_89 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (987) all_57_1_89 = all_47_2_83 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (988) all_57_1_89 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (989) all_57_1_89 = all_24_0_28 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (990) all_57_1_89 = all_26_2_33 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (991) all_57_1_89 = all_24_2_30 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (992) all_57_1_89 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.91  												| (993) all_57_1_89 = all_52_2_87 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.91  												|
% 219.91/170.91  												| Instantiating formula (28) with xn, all_57_1_89, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (994) all_72_1_100 = all_57_1_89 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (995) all_67_1_96 = all_57_1_89 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (996) all_57_1_89 = all_47_1_82 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (997) all_57_1_89 = all_39_7_73 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (998) all_57_1_89 = all_37_3_64 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (999) all_57_1_89 = all_22_1_26 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (1000) all_57_1_89 = all_20_1_23 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (1001) all_57_1_89 = all_18_1_20 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (1002) all_57_1_89 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (1003) all_57_1_89 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (1004) all_57_1_89 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_57_1_89, all_62_1_93 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, aNaturalNumber0(xn) = all_57_1_89, yields:
% 219.91/170.92  												| (1005) all_62_1_93 = all_57_1_89
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with sz10, all_39_8_74, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.92  												| (1006) all_39_8_74 = 0 |  ~ (aNaturalNumber0(sz10) = all_39_8_74)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with sz00, all_39_8_74, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.92  												| (1007) all_39_8_74 = 0 |  ~ (aNaturalNumber0(sz00) = all_39_8_74)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1008) all_82_2_109 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1009) all_67_2_97 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1010) all_39_8_74 = all_20_0_22 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1011) all_77_2_105 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1012) all_47_2_83 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1013) all_39_8_74 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1014) all_39_8_74 = all_24_0_28 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1015) all_39_8_74 = all_26_2_33 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1016) all_39_8_74 = all_24_2_30 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1017) all_39_8_74 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1018) all_52_2_87 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1019) all_72_1_100 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1020) all_67_1_96 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1021) all_47_1_82 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1022) all_39_7_73 = all_39_8_74 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1023) all_39_8_74 = all_37_3_64 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1024) all_39_8_74 = all_22_1_26 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1025) all_39_8_74 = all_20_1_23 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1026) all_39_8_74 = all_18_1_20 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1027) all_39_8_74 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1028) all_39_8_74 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1029) all_39_8_74 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_39_8_74, all_62_1_93 and discharging atoms aNaturalNumber0(xn) = all_62_1_93, aNaturalNumber0(xn) = all_39_8_74, yields:
% 219.91/170.92  												| (1030) all_62_1_93 = all_39_8_74
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with sz00, all_37_4_65, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.92  												| (1031) all_37_4_65 = 0 |  ~ (aNaturalNumber0(sz00) = all_37_4_65)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1032) all_82_2_109 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1033) all_67_2_97 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1034) all_37_4_65 = all_20_0_22 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1035) all_77_2_105 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1036) all_47_2_83 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1037) all_37_4_65 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1038) all_37_4_65 = all_24_0_28 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1039) all_37_4_65 = all_26_2_33 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1040) all_37_4_65 = all_24_2_30 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1041) all_37_4_65 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1042) all_52_2_87 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1043) all_72_1_100 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1044) all_67_1_96 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1045) all_47_1_82 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1046) all_39_7_73 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1047) all_37_3_64 = all_37_4_65 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1048) all_37_4_65 = all_22_1_26 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1049) all_37_4_65 = all_20_1_23 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1050) all_37_4_65 = all_18_1_20 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1051) all_37_4_65 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1052) all_37_4_65 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1053) all_37_4_65 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_37_4_65, all_77_1_104 and discharging atoms aNaturalNumber0(xn) = all_77_1_104, aNaturalNumber0(xn) = all_37_4_65, yields:
% 219.91/170.92  												| (1054) all_77_1_104 = all_37_4_65
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with sz10, all_18_2_21, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.92  												| (1055) all_18_2_21 = 0 |  ~ (aNaturalNumber0(sz10) = all_18_2_21)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with sz00, all_18_2_21, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.92  												| (1056) all_18_2_21 = 0 |  ~ (aNaturalNumber0(sz00) = all_18_2_21)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1057) all_82_2_109 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1058) all_67_2_97 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1059) all_20_0_22 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1060) all_77_2_105 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1061) all_18_2_21 = all_16_0_16 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1062) all_24_0_28 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1063) all_26_2_33 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1064) all_24_2_30 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1065) all_18_2_21 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1066) all_52_2_87 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1067) all_72_1_100 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.92  												| (1068) all_67_1_96 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.92  												|
% 219.91/170.92  												| Instantiating formula (28) with xn, all_18_2_21, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1069) all_47_1_82 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1070) all_39_7_73 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1071) all_37_3_64 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1072) all_22_1_26 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1073) all_18_1_20 = all_18_2_21 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1074) all_18_2_21 = all_16_1_17 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1075) all_18_2_21 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1076) all_18_2_21 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_57_1_89 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1077) all_57_1_89 = all_18_2_21
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_18_2_21, all_37_4_65 and discharging atoms aNaturalNumber0(xn) = all_37_4_65, aNaturalNumber0(xn) = all_18_2_21, yields:
% 219.91/170.93  												| (1078) all_37_4_65 = all_18_2_21
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with sz10, all_16_2_18, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.93  												| (1079) all_16_2_18 = 0 |  ~ (aNaturalNumber0(sz10) = all_16_2_18)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with sz00, all_16_2_18, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.93  												| (1080) all_16_2_18 = 0 |  ~ (aNaturalNumber0(sz00) = all_16_2_18)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1081) all_82_2_109 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1082) all_67_2_97 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1083) all_20_0_22 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1084) all_77_2_105 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1085) all_47_2_83 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1086) all_16_0_16 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1087) all_24_0_28 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1088) all_26_2_33 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1089) all_24_2_30 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1090) all_16_2_18 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1091) all_52_2_87 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1092) all_72_1_100 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1093) all_67_1_96 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1094) all_47_1_82 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1095) all_39_7_73 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1096) all_37_3_64 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1097) all_22_1_26 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1098) all_20_1_23 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1099) all_18_1_20 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1100) all_16_1_17 = all_16_2_18 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1101) all_16_2_18 = all_14_1_14 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1102) all_16_2_18 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_16_2_18, all_18_2_21 and discharging atoms aNaturalNumber0(xn) = all_18_2_21, aNaturalNumber0(xn) = all_16_2_18, yields:
% 219.91/170.93  												| (1103) all_18_2_21 = all_16_2_18
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with sz10, all_14_2_15, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.93  												| (1104) all_14_2_15 = 0 |  ~ (aNaturalNumber0(sz10) = all_14_2_15)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with sz00, all_14_2_15, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.93  												| (1105) all_14_2_15 = 0 |  ~ (aNaturalNumber0(sz00) = all_14_2_15)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1106) all_82_2_109 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1107) all_67_2_97 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1108) all_20_0_22 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1109) all_77_2_105 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1110) all_47_2_83 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1111) all_16_0_16 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1112) all_24_0_28 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1113) all_26_2_33 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1114) all_24_2_30 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1115) all_14_2_15 = all_12_0_10 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1116) all_52_2_87 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1117) all_72_1_100 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1118) all_67_1_96 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1119) all_47_1_82 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1120) all_39_7_73 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1121) all_37_3_64 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1122) all_22_1_26 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1123) all_20_1_23 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1124) all_18_1_20 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1125) all_16_1_17 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1126) all_14_1_14 = all_14_2_15 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1127) all_14_2_15 = all_12_1_11 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_14_2_15, all_57_1_89 and discharging atoms aNaturalNumber0(xn) = all_57_1_89, aNaturalNumber0(xn) = all_14_2_15, yields:
% 219.91/170.93  												| (1128) all_57_1_89 = all_14_2_15
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with sz10, all_12_2_12, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 219.91/170.93  												| (1129) all_12_2_12 = 0 |  ~ (aNaturalNumber0(sz10) = all_12_2_12)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with sz00, all_12_2_12, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 219.91/170.93  												| (1130) all_12_2_12 = 0 |  ~ (aNaturalNumber0(sz00) = all_12_2_12)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_82_2_109 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1131) all_82_2_109 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_67_2_97 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1132) all_67_2_97 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_20_0_22 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1133) all_20_0_22 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_77_2_105 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1134) all_77_2_105 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_47_2_83 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1135) all_47_2_83 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_16_0_16 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1136) all_16_0_16 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_24_0_28 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1137) all_24_0_28 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_26_2_33 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1138) all_26_2_33 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_24_2_30 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1139) all_24_2_30 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_12_0_10 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1140) all_12_0_10 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_52_2_87 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1141) all_52_2_87 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_72_1_100 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1142) all_72_1_100 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_67_1_96 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.93  												| (1143) all_67_1_96 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 219.91/170.93  												|
% 219.91/170.93  												| Instantiating formula (28) with xn, all_12_2_12, all_47_1_82 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1144) all_47_1_82 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_39_7_73 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1145) all_39_7_73 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_37_3_64 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1146) all_37_3_64 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_22_1_26 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1147) all_22_1_26 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_20_1_23 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1148) all_20_1_23 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_18_1_20 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1149) all_18_1_20 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_16_1_17 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1150) all_16_1_17 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_14_1_14 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1151) all_14_1_14 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_12_1_11 and discharging atoms aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1152) all_12_1_11 = all_12_2_12 |  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 219.91/170.94  												|
% 219.91/170.94  												| Instantiating formula (28) with xn, all_12_2_12, all_82_1_108 and discharging atoms aNaturalNumber0(xn) = all_82_1_108, aNaturalNumber0(xn) = all_12_2_12, yields:
% 219.91/170.94  												| (1153) all_82_1_108 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (955,1153) yields a new equation:
% 219.91/170.94  												| (1154) all_77_1_104 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1154 yields:
% 219.91/170.94  												| (1155) all_77_1_104 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (330,322) yields a new equation:
% 219.91/170.94  												| (1156) all_67_2_97 = all_20_0_22
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (549,678) yields a new equation:
% 219.91/170.94  												| (1157) all_77_3_106 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1157 yields:
% 219.91/170.94  												| (1158) all_77_3_106 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1054,1155) yields a new equation:
% 219.91/170.94  												| (1159) all_37_4_65 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1159 yields:
% 219.91/170.94  												| (1160) all_37_4_65 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (408,424) yields a new equation:
% 219.91/170.94  												| (1161) all_47_2_83 = all_16_0_16
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1161 yields:
% 219.91/170.94  												| (1162) all_47_2_83 = all_16_0_16
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (565,1158) yields a new equation:
% 219.91/170.94  												| (1163) all_72_3_102 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1163 yields:
% 219.91/170.94  												| (1164) all_72_3_102 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (732,810) yields a new equation:
% 219.91/170.94  												| (1165) all_67_1_96 = all_22_1_26
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1165 yields:
% 219.91/170.94  												| (1166) all_67_1_96 = all_22_1_26
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (349,378) yields a new equation:
% 219.91/170.94  												| (1167) all_62_2_94 = all_20_2_24
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1167 yields:
% 219.91/170.94  												| (1168) all_62_2_94 = all_20_2_24
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (581,1164) yields a new equation:
% 219.91/170.94  												| (1169) all_67_3_98 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1169 yields:
% 219.91/170.94  												| (1170) all_67_3_98 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (789,1166) yields a new equation:
% 219.91/170.94  												| (1171) all_37_3_64 = all_22_1_26
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1171 yields:
% 219.91/170.94  												| (1172) all_37_3_64 = all_22_1_26
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (628,1170) yields a new equation:
% 219.91/170.94  												| (1173) all_47_3_84 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1173 yields:
% 219.91/170.94  												| (1174) all_47_3_84 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1005,1030) yields a new equation:
% 219.91/170.94  												| (1175) all_57_1_89 = all_39_8_74
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1175 yields:
% 219.91/170.94  												| (1176) all_57_1_89 = all_39_8_74
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (358,1168) yields a new equation:
% 219.91/170.94  												| (1177) all_57_2_90 = all_20_2_24
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1177 yields:
% 219.91/170.94  												| (1178) all_57_2_90 = all_20_2_24
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (980,1176) yields a new equation:
% 219.91/170.94  												| (1179) all_39_8_74 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1128,1176) yields a new equation:
% 219.91/170.94  												| (1180) all_39_8_74 = all_14_2_15
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1077,1176) yields a new equation:
% 219.91/170.94  												| (1181) all_39_8_74 = all_18_2_21
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (368,1178) yields a new equation:
% 219.91/170.94  												| (1182) all_22_2_27 = all_20_2_24
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1182 yields:
% 219.91/170.94  												| (1183) all_22_2_27 = all_20_2_24
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (612,694) yields a new equation:
% 219.91/170.94  												| (1184) all_52_1_86 = all_24_1_29
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1184 yields:
% 219.91/170.94  												| (1185) all_52_1_86 = all_24_1_29
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (660,1185) yields a new equation:
% 219.91/170.94  												| (1186) all_37_2_63 = all_24_1_29
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1186 yields:
% 219.91/170.94  												| (1187) all_37_2_63 = all_24_1_29
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (907,827) yields a new equation:
% 219.91/170.94  												| (1188) all_20_1_23 = all_12_1_11
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (887,827) yields a new equation:
% 219.91/170.94  												| (1189) all_20_1_23 = all_14_1_14
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (790,827) yields a new equation:
% 219.91/170.94  												| (1190) all_37_3_64 = all_20_1_23
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1190 yields:
% 219.91/170.94  												| (1191) all_37_3_64 = all_20_1_23
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (661,1174) yields a new equation:
% 219.91/170.94  												| (1192) all_37_2_63 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1192 yields:
% 219.91/170.94  												| (1193) all_37_2_63 = all_26_1_32
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (662,629) yields a new equation:
% 219.91/170.94  												| (1194) all_37_2_63 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1194 yields:
% 219.91/170.94  												| (1195) all_37_2_63 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (791,847) yields a new equation:
% 219.91/170.94  												| (1196) all_37_3_64 = all_18_1_20
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1196 yields:
% 219.91/170.94  												| (1197) all_37_3_64 = all_18_1_20
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1181,1180) yields a new equation:
% 219.91/170.94  												| (1198) all_18_2_21 = all_14_2_15
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1198 yields:
% 219.91/170.94  												| (1199) all_18_2_21 = all_14_2_15
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1179,1180) yields a new equation:
% 219.91/170.94  												| (1200) all_14_2_15 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1187,1193) yields a new equation:
% 219.91/170.94  												| (1201) all_26_1_32 = all_24_1_29
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1195,1193) yields a new equation:
% 219.91/170.94  												| (1202) all_26_1_32 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1191,1172) yields a new equation:
% 219.91/170.94  												| (1203) all_22_1_26 = all_20_1_23
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1197,1172) yields a new equation:
% 219.91/170.94  												| (1204) all_22_1_26 = all_18_1_20
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1078,1160) yields a new equation:
% 219.91/170.94  												| (1205) all_18_2_21 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1205 yields:
% 219.91/170.94  												| (1206) all_18_2_21 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1202,1201) yields a new equation:
% 219.91/170.94  												| (1207) all_24_1_29 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (500,480) yields a new equation:
% 219.91/170.94  												| (1208) all_24_2_30 = all_12_0_10
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1203,1204) yields a new equation:
% 219.91/170.94  												| (1209) all_20_1_23 = all_18_1_20
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1209 yields:
% 219.91/170.94  												| (1210) all_20_1_23 = all_18_1_20
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1189,1210) yields a new equation:
% 219.91/170.94  												| (1211) all_18_1_20 = all_14_1_14
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1188,1210) yields a new equation:
% 219.91/170.94  												| (1212) all_18_1_20 = all_12_1_11
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1211,1212) yields a new equation:
% 219.91/170.94  												| (1213) all_14_1_14 = all_12_1_11
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1213 yields:
% 219.91/170.94  												| (1214) all_14_1_14 = all_12_1_11
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1199,1103) yields a new equation:
% 219.91/170.94  												| (1215) all_16_2_18 = all_14_2_15
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1206,1103) yields a new equation:
% 219.91/170.94  												| (1216) all_16_2_18 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (888,848) yields a new equation:
% 219.91/170.94  												| (1217) all_14_1_14 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1217 yields:
% 219.91/170.94  												| (1218) all_14_1_14 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1215,1216) yields a new equation:
% 219.91/170.94  												| (1219) all_14_2_15 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1219 yields:
% 219.91/170.94  												| (1220) all_14_2_15 = all_12_2_12
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1218,1214) yields a new equation:
% 219.91/170.94  												| (1221) all_12_1_11 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1220,1200) yields a new equation:
% 219.91/170.94  												| (1222) all_12_2_12 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Simplifying 1222 yields:
% 219.91/170.94  												| (1223) all_12_2_12 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1221,1214) yields a new equation:
% 219.91/170.94  												| (1218) all_14_1_14 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1223,1216) yields a new equation:
% 219.91/170.94  												| (1225) all_16_2_18 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1225,1103) yields a new equation:
% 219.91/170.94  												| (1226) all_18_2_21 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1221,1212) yields a new equation:
% 219.91/170.94  												| (1227) all_18_1_20 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1227,1210) yields a new equation:
% 219.91/170.94  												| (1228) all_20_1_23 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1227,1204) yields a new equation:
% 219.91/170.94  												| (1229) all_22_1_26 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1208,480) yields a new equation:
% 219.91/170.94  												| (500) all_26_2_33 = all_12_0_10
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1207,1201) yields a new equation:
% 219.91/170.94  												| (1202) all_26_1_32 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1223,1160) yields a new equation:
% 219.91/170.94  												| (1232) all_37_4_65 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1229,1172) yields a new equation:
% 219.91/170.94  												| (1233) all_37_3_64 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1202,1193) yields a new equation:
% 219.91/170.94  												| (1195) all_37_2_63 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1200,1180) yields a new equation:
% 219.91/170.94  												| (1179) all_39_8_74 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1227,847) yields a new equation:
% 219.91/170.94  												| (1236) all_39_7_73 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1228,827) yields a new equation:
% 219.91/170.94  												| (1237) all_47_1_82 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1207,1185) yields a new equation:
% 219.91/170.94  												| (1238) all_52_1_86 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1179,1176) yields a new equation:
% 219.91/170.94  												| (980) all_57_1_89 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1179,1030) yields a new equation:
% 219.91/170.94  												| (1240) all_62_1_93 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1202,1170) yields a new equation:
% 219.91/170.94  												| (1241) all_67_3_98 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1229,1166) yields a new equation:
% 219.91/170.94  												| (1242) all_67_1_96 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1202,1164) yields a new equation:
% 219.91/170.94  												| (1243) all_72_3_102 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1229,810) yields a new equation:
% 219.91/170.94  												| (1244) all_72_1_100 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1202,1158) yields a new equation:
% 219.91/170.94  												| (1245) all_77_3_106 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1223,1155) yields a new equation:
% 219.91/170.94  												| (1246) all_77_1_104 = 0
% 219.91/170.94  												|
% 219.91/170.94  												| Combining equations (1202,678) yields a new equation:
% 219.91/170.94  												| (1247) all_82_3_110 = 0
% 219.91/170.94  												|
% 219.91/170.95  												| Combining equations (1156,322) yields a new equation:
% 219.91/170.95  												| (330) all_82_2_109 = all_20_0_22
% 219.91/170.95  												|
% 219.91/170.95  												| Combining equations (1223,1153) yields a new equation:
% 219.91/170.95  												| (1249) all_82_1_108 = 0
% 219.91/170.95  												|
% 219.91/170.95  												| From (302) and (190) follows:
% 219.91/170.95  												| (53) isPrime0(xp) = 0
% 219.91/170.95  												|
% 219.91/170.95  												| From (307) and (186) follows:
% 219.91/170.95  												| (1251) doDivides0(xp, all_0_7_7) = all_39_3_69
% 219.91/170.95  												|
% 219.91/170.95  												| From (306) and (193) follows:
% 219.91/170.95  												| (51) doDivides0(xp, xn) = all_0_0_0
% 219.91/170.95  												|
% 219.91/170.95  												| From (307) and (192) follows:
% 219.91/170.95  												| (96) sdtasdt0(xn, xm) = all_0_7_7
% 219.91/170.95  												|
% 219.91/170.95  												| From (1156) and (243) follows:
% 219.91/170.95  												| (153) aNaturalNumber0(all_0_2_2) = all_20_0_22
% 219.91/170.95  												|
% 219.91/170.95  												| From (1183) and (159) follows:
% 219.91/170.95  												| (154) aNaturalNumber0(all_0_3_3) = all_20_2_24
% 219.91/170.95  												|
% 219.91/170.95  												| From (1162) and (204) follows:
% 219.91/170.95  												| (143) aNaturalNumber0(all_0_7_7) = all_16_0_16
% 219.91/170.95  												|
% 219.91/170.95  												| From (1208) and (164) follows:
% 219.91/170.95  												| (133) aNaturalNumber0(all_0_9_9) = all_12_0_10
% 219.91/170.95  												|
% 219.91/170.95  												| From (1207) and (165) follows:
% 219.91/170.95  												| (9) aNaturalNumber0(xp) = 0
% 219.91/170.95  												|
% 219.91/170.95  												| From (1221) and (134) follows:
% 219.91/170.95  												| (12) aNaturalNumber0(xm) = 0
% 219.91/170.95  												|
% 219.91/170.95  												| From (1223) and (135) follows:
% 219.91/170.95  												| (91) aNaturalNumber0(xn) = 0
% 219.91/170.95  												|
% 219.91/170.95  												+-Applying beta-rule and splitting (183), into two cases.
% 219.91/170.95  												|-Branch one:
% 219.91/170.95  												| (1261)  ~ (all_37_2_63 = 0)
% 219.91/170.95  												|
% 219.91/170.95  													| Equations (1195) can reduce 1261 to:
% 219.91/170.95  													| (197) $false
% 219.91/170.95  													|
% 219.91/170.95  													|-The branch is then unsatisfiable
% 219.91/170.95  												|-Branch two:
% 219.91/170.95  												| (1195) all_37_2_63 = 0
% 219.91/170.95  												| (1264)  ~ (all_37_3_64 = 0) |  ~ (all_37_4_65 = 0) | all_37_0_61 = all_0_8_8
% 219.91/170.95  												|
% 219.91/170.95  													+-Applying beta-rule and splitting (151), into two cases.
% 219.91/170.95  													|-Branch one:
% 219.91/170.95  													| (1265)  ~ (all_18_1_20 = 0)
% 219.91/170.95  													|
% 219.91/170.95  														| Equations (1227) can reduce 1265 to:
% 219.91/170.95  														| (197) $false
% 219.91/170.95  														|
% 219.91/170.95  														|-The branch is then unsatisfiable
% 219.91/170.95  													|-Branch two:
% 219.91/170.95  													| (1227) all_18_1_20 = 0
% 219.91/170.95  													| (1268)  ~ (all_18_2_21 = 0) | all_18_0_19 = all_0_7_7
% 219.91/170.95  													|
% 219.91/170.95  														+-Applying beta-rule and splitting (136), into two cases.
% 219.91/170.95  														|-Branch one:
% 219.91/170.95  														| (1269)  ~ (all_12_1_11 = 0)
% 219.91/170.95  														|
% 219.91/170.95  															| Equations (1221) can reduce 1269 to:
% 219.91/170.95  															| (197) $false
% 219.91/170.95  															|
% 219.91/170.95  															|-The branch is then unsatisfiable
% 219.91/170.95  														|-Branch two:
% 219.91/170.95  														| (1221) all_12_1_11 = 0
% 219.91/170.95  														| (1272)  ~ (all_12_2_12 = 0) | all_12_0_10 = 0
% 219.91/170.95  														|
% 219.91/170.95  															+-Applying beta-rule and splitting (1268), into two cases.
% 219.91/170.95  															|-Branch one:
% 219.91/170.95  															| (1273)  ~ (all_18_2_21 = 0)
% 219.91/170.95  															|
% 219.91/170.95  																| Equations (1226) can reduce 1273 to:
% 219.91/170.95  																| (197) $false
% 219.91/170.95  																|
% 219.91/170.95  																|-The branch is then unsatisfiable
% 219.91/170.95  															|-Branch two:
% 219.91/170.95  															| (1226) all_18_2_21 = 0
% 219.91/170.95  															| (1276) all_18_0_19 = all_0_7_7
% 219.91/170.95  															|
% 219.91/170.95  																| From (1276) and (148) follows:
% 219.91/170.95  																| (1277) sdtasdt0(xm, xn) = all_0_7_7
% 219.91/170.95  																|
% 219.91/170.95  																+-Applying beta-rule and splitting (1272), into two cases.
% 219.91/170.95  																|-Branch one:
% 219.91/170.95  																| (1278)  ~ (all_12_2_12 = 0)
% 219.91/170.95  																|
% 219.91/170.95  																	| Equations (1223) can reduce 1278 to:
% 219.91/170.95  																	| (197) $false
% 219.91/170.95  																	|
% 219.91/170.95  																	|-The branch is then unsatisfiable
% 219.91/170.95  																|-Branch two:
% 219.91/170.95  																| (1223) all_12_2_12 = 0
% 219.91/170.95  																| (1281) all_12_0_10 = 0
% 219.91/170.95  																|
% 219.91/170.95  																	| Combining equations (1281,1208) yields a new equation:
% 219.91/170.95  																	| (1282) all_24_2_30 = 0
% 219.91/170.95  																	|
% 219.91/170.95  																	| Combining equations (1281,500) yields a new equation:
% 219.91/170.95  																	| (1283) all_26_2_33 = 0
% 219.91/170.95  																	|
% 219.91/170.95  																	| From (1281) and (133) follows:
% 219.91/170.95  																	| (1284) aNaturalNumber0(all_0_9_9) = 0
% 219.91/170.95  																	|
% 219.91/170.95  																	+-Applying beta-rule and splitting (146), into two cases.
% 219.91/170.95  																	|-Branch one:
% 219.91/170.95  																	| (1285)  ~ (all_16_1_17 = 0)
% 219.91/170.95  																	|
% 219.91/170.95  																		| Equations (848) can reduce 1285 to:
% 219.91/170.95  																		| (197) $false
% 219.91/170.95  																		|
% 219.91/170.95  																		|-The branch is then unsatisfiable
% 219.91/170.95  																	|-Branch two:
% 219.91/170.95  																	| (848) all_16_1_17 = 0
% 219.91/170.95  																	| (1288)  ~ (all_16_2_18 = 0) | all_16_0_16 = 0
% 219.91/170.95  																	|
% 219.91/170.95  																		+-Applying beta-rule and splitting (1288), into two cases.
% 219.91/170.95  																		|-Branch one:
% 219.91/170.95  																		| (1289)  ~ (all_16_2_18 = 0)
% 219.91/170.95  																		|
% 219.91/170.95  																			| Equations (1225) can reduce 1289 to:
% 219.91/170.95  																			| (197) $false
% 219.91/170.95  																			|
% 219.91/170.95  																			|-The branch is then unsatisfiable
% 219.91/170.95  																		|-Branch two:
% 219.91/170.95  																		| (1225) all_16_2_18 = 0
% 219.91/170.95  																		| (1292) all_16_0_16 = 0
% 219.91/170.95  																		|
% 219.91/170.95  																			| Combining equations (1292,1162) yields a new equation:
% 219.91/170.95  																			| (1293) all_47_2_83 = 0
% 219.91/170.95  																			|
% 219.91/170.95  																			| Combining equations (1292,424) yields a new equation:
% 219.91/170.95  																			| (1294) all_77_2_105 = 0
% 219.91/170.95  																			|
% 219.91/170.95  																			| From (1292) and (143) follows:
% 219.91/170.95  																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 219.91/170.95  																			|
% 219.91/170.95  																			+-Applying beta-rule and splitting (175), into two cases.
% 219.91/170.95  																			|-Branch one:
% 219.91/170.95  																			| (1296) all_33_0_49 = xp & all_33_1_50 = 0 & sdtpldt0(xm, all_33_2_51) = xp & aNaturalNumber0(all_33_2_51) = 0
% 219.91/170.95  																			|
% 219.91/170.95  																				| Applying alpha-rule on (1296) yields:
% 219.91/170.95  																				| (1297) all_33_0_49 = xp
% 219.91/170.95  																				| (1298) all_33_1_50 = 0
% 219.91/170.95  																				| (1299) sdtpldt0(xm, all_33_2_51) = xp
% 219.91/170.95  																				| (1300) aNaturalNumber0(all_33_2_51) = 0
% 219.91/170.95  																				|
% 219.91/170.95  																				+-Applying beta-rule and splitting (172), into two cases.
% 219.91/170.95  																				|-Branch one:
% 219.91/170.95  																				| (1301) all_28_0_34 = all_0_7_7 & all_28_1_35 = 0 & sdtasdt0(xp, all_28_2_36) = all_0_7_7 & aNaturalNumber0(all_28_2_36) = 0
% 219.91/170.95  																				|
% 219.91/170.95  																					| Applying alpha-rule on (1301) yields:
% 219.91/170.95  																					| (1302) all_28_0_34 = all_0_7_7
% 219.91/170.95  																					| (1303) all_28_1_35 = 0
% 219.91/170.95  																					| (1304) sdtasdt0(xp, all_28_2_36) = all_0_7_7
% 219.91/170.95  																					| (1305) aNaturalNumber0(all_28_2_36) = 0
% 219.91/170.95  																					|
% 219.91/170.95  																					+-Applying beta-rule and splitting (141), into two cases.
% 219.91/170.95  																					|-Branch one:
% 219.91/170.95  																					| (1306)  ~ (all_14_1_14 = 0)
% 219.91/170.95  																					|
% 219.91/170.95  																						| Equations (1218) can reduce 1306 to:
% 219.91/170.95  																						| (197) $false
% 219.91/170.95  																						|
% 219.91/170.95  																						|-The branch is then unsatisfiable
% 219.91/170.95  																					|-Branch two:
% 219.91/170.95  																					| (1218) all_14_1_14 = 0
% 219.91/170.95  																					| (1309)  ~ (all_14_2_15 = 0) | all_14_0_13 = all_0_9_9
% 219.91/170.95  																					|
% 219.91/170.95  																						+-Applying beta-rule and splitting (304), into two cases.
% 219.91/170.95  																						|-Branch one:
% 219.91/170.95  																						| (1310)  ~ (doDivides0(xp, all_0_7_7) = all_39_3_69)
% 219.91/170.95  																						|
% 219.91/170.95  																							| Using (1251) and (1310) yields:
% 219.91/170.95  																							| (1311) $false
% 219.91/170.95  																							|
% 219.91/170.95  																							|-The branch is then unsatisfiable
% 219.91/170.95  																						|-Branch two:
% 219.91/170.95  																						| (1251) doDivides0(xp, all_0_7_7) = all_39_3_69
% 219.91/170.95  																						| (1313) all_39_3_69 = 0
% 219.91/170.95  																						|
% 219.91/170.95  																							| From (1313) and (1251) follows:
% 219.91/170.95  																							| (37) doDivides0(xp, all_0_7_7) = 0
% 219.91/170.95  																							|
% 219.91/170.95  																							+-Applying beta-rule and splitting (173), into two cases.
% 219.91/170.95  																							|-Branch one:
% 219.91/170.95  																							| (1315) all_30_0_40 = xp & all_30_1_41 = 0 & sdtpldt0(xn, all_30_2_42) = xp & aNaturalNumber0(all_30_2_42) = 0
% 219.91/170.95  																							|
% 219.91/170.95  																								| Applying alpha-rule on (1315) yields:
% 219.91/170.95  																								| (1316) all_30_0_40 = xp
% 219.91/170.95  																								| (1317) all_30_1_41 = 0
% 219.91/170.95  																								| (1318) sdtpldt0(xn, all_30_2_42) = xp
% 219.91/170.95  																								| (1319) aNaturalNumber0(all_30_2_42) = 0
% 219.91/170.95  																								|
% 219.91/170.95  																								+-Applying beta-rule and splitting (1264), into two cases.
% 219.91/170.95  																								|-Branch one:
% 219.91/170.95  																								| (1320)  ~ (all_37_3_64 = 0)
% 219.91/170.95  																								|
% 219.91/170.95  																									| Equations (1233) can reduce 1320 to:
% 219.91/170.95  																									| (197) $false
% 219.91/170.95  																									|
% 219.91/170.95  																									|-The branch is then unsatisfiable
% 219.91/170.95  																								|-Branch two:
% 219.91/170.95  																								| (1233) all_37_3_64 = 0
% 219.91/170.95  																								| (1323)  ~ (all_37_4_65 = 0) | all_37_0_61 = all_0_8_8
% 219.91/170.95  																								|
% 219.91/170.95  																									+-Applying beta-rule and splitting (1323), into two cases.
% 219.91/170.95  																									|-Branch one:
% 219.91/170.95  																									| (1324)  ~ (all_37_4_65 = 0)
% 219.91/170.95  																									|
% 219.91/170.95  																										| Equations (1232) can reduce 1324 to:
% 219.91/170.95  																										| (197) $false
% 219.91/170.95  																										|
% 219.91/170.95  																										|-The branch is then unsatisfiable
% 219.91/170.95  																									|-Branch two:
% 219.91/170.95  																									| (1232) all_37_4_65 = 0
% 219.91/170.95  																									| (1327) all_37_0_61 = all_0_8_8
% 219.91/170.95  																									|
% 219.91/170.95  																										| From (1327) and (178) follows:
% 219.91/170.95  																										| (1328) sdtpldt0(xn, all_37_1_62) = all_0_8_8
% 219.91/170.95  																										|
% 219.91/170.95  																										+-Applying beta-rule and splitting (1309), into two cases.
% 219.91/170.95  																										|-Branch one:
% 219.91/170.95  																										| (1329)  ~ (all_14_2_15 = 0)
% 219.91/170.95  																										|
% 219.91/170.95  																											| Equations (1200) can reduce 1329 to:
% 219.91/170.95  																											| (197) $false
% 219.91/170.95  																											|
% 219.91/170.95  																											|-The branch is then unsatisfiable
% 219.91/170.95  																										|-Branch two:
% 219.91/170.95  																										| (1200) all_14_2_15 = 0
% 219.91/170.95  																										| (1332) all_14_0_13 = all_0_9_9
% 219.91/170.95  																										|
% 219.91/170.95  																											| From (1332) and (138) follows:
% 219.91/170.95  																											| (1333) sdtpldt0(xm, xn) = all_0_9_9
% 219.91/170.95  																											|
% 219.91/170.95  																											+-Applying beta-rule and splitting (166), into two cases.
% 219.91/170.95  																											|-Branch one:
% 219.91/170.95  																											| (1334)  ~ (all_24_1_29 = 0)
% 219.91/170.95  																											|
% 219.91/170.95  																												| Equations (1207) can reduce 1334 to:
% 219.91/170.95  																												| (197) $false
% 219.91/170.95  																												|
% 219.91/170.95  																												|-The branch is then unsatisfiable
% 219.91/170.95  																											|-Branch two:
% 219.91/170.95  																											| (1207) all_24_1_29 = 0
% 219.91/170.95  																											| (1337)  ~ (all_24_2_30 = 0) | all_24_0_28 = 0
% 219.91/170.95  																											|
% 219.91/170.95  																												+-Applying beta-rule and splitting (176), into two cases.
% 219.91/170.95  																												|-Branch one:
% 219.91/170.95  																												| (1338) all_34_0_52 = xn & all_34_1_53 = 0 & sdtasdt0(xr, all_34_2_54) = xn & aNaturalNumber0(all_34_2_54) = 0
% 219.91/170.95  																												|
% 219.91/170.95  																													| Applying alpha-rule on (1338) yields:
% 219.91/170.95  																													| (1339) all_34_0_52 = xn
% 219.91/170.95  																													| (1340) all_34_1_53 = 0
% 219.91/170.95  																													| (1341) sdtasdt0(xr, all_34_2_54) = xn
% 219.91/170.95  																													| (1342) aNaturalNumber0(all_34_2_54) = 0
% 219.91/170.95  																													|
% 219.91/170.95  																													+-Applying beta-rule and splitting (171), into two cases.
% 219.91/170.95  																													|-Branch one:
% 219.91/170.95  																													| (1343)  ~ (all_26_1_32 = 0)
% 219.91/170.95  																													|
% 219.91/170.95  																														| Equations (1202) can reduce 1343 to:
% 219.91/170.95  																														| (197) $false
% 219.91/170.95  																														|
% 219.91/170.95  																														|-The branch is then unsatisfiable
% 219.91/170.95  																													|-Branch two:
% 219.91/170.95  																													| (1202) all_26_1_32 = 0
% 219.91/170.95  																													| (1346)  ~ (all_26_2_33 = 0) | all_26_0_31 = all_0_8_8
% 219.91/170.95  																													|
% 219.91/170.95  																														+-Applying beta-rule and splitting (1337), into two cases.
% 219.91/170.95  																														|-Branch one:
% 219.91/170.95  																														| (1347)  ~ (all_24_2_30 = 0)
% 219.91/170.95  																														|
% 219.91/170.95  																															| Equations (1282) can reduce 1347 to:
% 219.91/170.95  																															| (197) $false
% 219.91/170.95  																															|
% 219.91/170.95  																															|-The branch is then unsatisfiable
% 219.91/170.95  																														|-Branch two:
% 219.91/170.95  																														| (1282) all_24_2_30 = 0
% 219.91/170.95  																														| (1350) all_24_0_28 = 0
% 219.91/170.95  																														|
% 219.91/170.95  																															| From (1350) and (163) follows:
% 219.91/170.95  																															| (1351) aNaturalNumber0(all_0_8_8) = 0
% 219.91/170.96  																															|
% 219.91/170.96  																															+-Applying beta-rule and splitting (1346), into two cases.
% 219.91/170.96  																															|-Branch one:
% 219.91/170.96  																															| (1352)  ~ (all_26_2_33 = 0)
% 219.91/170.96  																															|
% 219.91/170.96  																																| Equations (1283) can reduce 1352 to:
% 219.91/170.96  																																| (197) $false
% 219.91/170.96  																																|
% 219.91/170.96  																																|-The branch is then unsatisfiable
% 219.91/170.96  																															|-Branch two:
% 219.91/170.96  																															| (1283) all_26_2_33 = 0
% 219.91/170.96  																															| (1355) all_26_0_31 = all_0_8_8
% 219.91/170.96  																															|
% 219.91/170.96  																																| From (1355) and (168) follows:
% 219.91/170.96  																																| (1356) sdtpldt0(xp, all_0_9_9) = all_0_8_8
% 219.91/170.96  																																|
% 219.91/170.96  																																+-Applying beta-rule and splitting (195), into two cases.
% 219.91/170.96  																																|-Branch one:
% 219.91/170.96  																																| (1357) all_41_0_75 = all_0_7_7 & all_41_1_76 = 0 & sdtasdt0(xr, all_41_2_77) = all_0_7_7 & aNaturalNumber0(all_41_2_77) = 0
% 219.91/170.96  																																|
% 219.91/170.96  																																	| Applying alpha-rule on (1357) yields:
% 219.91/170.96  																																	| (1358) all_41_0_75 = all_0_7_7
% 219.91/170.96  																																	| (1359) all_41_1_76 = 0
% 219.91/170.96  																																	| (1360) sdtasdt0(xr, all_41_2_77) = all_0_7_7
% 219.91/170.96  																																	| (1361) aNaturalNumber0(all_41_2_77) = 0
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (30) with all_99_0_112, xp and discharging atoms isPrime0(xp) = 0, doDivides0(all_99_0_112, xp) = 0, yields:
% 219.91/170.96  																																	| (1362) all_99_0_112 = xp | all_99_0_112 = sz10 |  ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_99_0_112) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (24) with xp, all_99_0_112 and discharging atoms doDivides0(all_99_0_112, xp) = 0, yields:
% 219.91/170.96  																																	| (1363)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = xp & v1 = 0 & sdtasdt0(all_99_0_112, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_99_0_112) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (30) with all_94_0_111, xr and discharging atoms isPrime0(xr) = 0, doDivides0(all_94_0_111, xr) = 0, yields:
% 219.91/170.96  																																	| (1364) all_94_0_111 = xr | all_94_0_111 = sz10 |  ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_94_0_111) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (52) with xm, all_72_0_99, xm, all_0_3_3 and discharging atoms doDivides0(all_0_3_3, xm) = all_72_0_99, yields:
% 219.91/170.96  																																	| (1365) all_72_0_99 = 0 |  ~ (sdtasdt0(all_0_3_3, xm) = xm) |  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(xm) = v0) | (aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (20) with all_52_0_85, xk, xp and discharging atoms sdtlseqdt0(xp, xk) = all_52_0_85, yields:
% 219.91/170.96  																																	| (1366) all_52_0_85 = 0 | xk = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (58) with all_62_0_92, all_0_3_3, xp, xn and discharging atoms sdtlseqdt0(xn, all_0_3_3) = all_62_0_92, sdtlseqdt0(xn, xp) = 0, yields:
% 219.91/170.96  																																	| (1367) all_62_0_92 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtlseqdt0(xp, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (73) with all_0_3_3, xn yields:
% 219.91/170.96  																																	| (1368) all_0_3_3 = xn |  ~ (sdtlseqdt0(xn, all_0_3_3) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(all_0_3_3, xn) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (21) with all_0_3_3, xn yields:
% 219.91/170.96  																																	| (1369)  ~ (sdtlseqdt0(xn, all_0_3_3) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = all_0_3_3 & v1 = 0 & sdtpldt0(xn, v0) = all_0_3_3 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (20) with all_62_0_92, all_0_3_3, xn and discharging atoms sdtlseqdt0(xn, all_0_3_3) = all_62_0_92, yields:
% 219.91/170.96  																																	| (1370) all_62_0_92 = 0 | all_0_3_3 = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (93) with all_0_7_7, all_41_2_77, xr and discharging atoms sdtasdt0(xr, all_41_2_77) = all_0_7_7, yields:
% 219.91/170.96  																																	| (1371)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(all_41_2_77, xr) = v2 & aNaturalNumber0(all_41_2_77) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_7_7))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (39) with all_34_2_54, all_0_3_3, xn, xr and discharging atoms sdtsldt0(xn, xr) = all_0_3_3, sdtasdt0(xr, all_34_2_54) = xn, yields:
% 219.91/170.96  																																	| (1372) all_34_2_54 = all_0_3_3 | xr = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_34_2_54) = v0) | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (76) with all_0_7_7, xn, xm, all_34_2_54, xr and discharging atoms sdtasdt0(xr, all_34_2_54) = xn, sdtasdt0(xn, xm) = all_0_7_7, yields:
% 219.91/170.96  																																	| (1373)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtasdt0(all_34_2_54, xm) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_34_2_54) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_7_7))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (93) with xn, all_34_2_54, xr and discharging atoms sdtasdt0(xr, all_34_2_54) = xn, yields:
% 219.91/170.96  																																	| (1374)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(all_34_2_54, xr) = v2 & aNaturalNumber0(all_34_2_54) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = xn))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (89) with all_0_6_6, xn, xp, all_28_2_36 and discharging atoms sdtlseqdt0(xp, xn) = all_0_6_6, yields:
% 219.91/170.96  																																	| (1375) all_28_2_36 = sz00 | all_0_6_6 = 0 |  ~ (sdtasdt0(xp, all_28_2_36) = xn) |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_28_2_36) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (39) with all_28_2_36, xk, all_0_7_7, xp and discharging atoms sdtsldt0(all_0_7_7, xp) = xk, sdtasdt0(xp, all_28_2_36) = all_0_7_7, yields:
% 219.91/170.96  																																	| (1376) all_28_2_36 = xk | xp = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_28_2_36) = v0) | (doDivides0(xp, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (52) with all_28_2_36, all_0_0_0, xn, xp and discharging atoms doDivides0(xp, xn) = all_0_0_0, yields:
% 219.91/170.96  																																	| (1377) all_0_0_0 = 0 |  ~ (sdtasdt0(xp, all_28_2_36) = xn) |  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_28_2_36) = v0) | (aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (50) with all_28_2_36, xp yields:
% 219.91/170.96  																																	| (1378) all_28_2_36 = sz00 | xp = sz00 |  ~ (sdtasdt0(xp, all_28_2_36) = sz00) |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_28_2_36) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (93) with all_0_7_7, all_28_2_36, xp and discharging atoms sdtasdt0(xp, all_28_2_36) = all_0_7_7, yields:
% 219.91/170.96  																																	| (1379)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(all_28_2_36, xp) = v2 & aNaturalNumber0(all_28_2_36) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_7_7))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (50) with all_0_3_3, xm yields:
% 219.91/170.96  																																	| (1380) all_0_3_3 = sz00 | xm = sz00 |  ~ (sdtasdt0(xm, all_0_3_3) = sz00) |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (93) with all_22_0_25, all_0_3_3, xm and discharging atoms sdtasdt0(xm, all_0_3_3) = all_22_0_25, yields:
% 219.91/170.96  																																	| (1381)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(all_0_3_3, xm) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_22_0_25))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (25) with all_22_0_25, all_0_3_3, xm and discharging atoms sdtasdt0(xm, all_0_3_3) = all_22_0_25, yields:
% 219.91/170.96  																																	| (1382)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_22_0_25) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (76) with all_0_7_7, xm, xn, xm, all_0_3_3 and discharging atoms sdtasdt0(xm, xn) = all_0_7_7, yields:
% 219.91/170.96  																																	| (1383)  ~ (sdtasdt0(all_0_3_3, xm) = xm) |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtasdt0(all_0_3_3, v3) = v4 & sdtasdt0(xm, xn) = v3 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_7_7))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (82) with all_0_7_7, all_22_0_25, xn, all_0_3_3, xm and discharging atoms sdtasdt0(xm, all_0_3_3) = all_22_0_25, sdtasdt0(xm, xn) = all_0_7_7, aNaturalNumber0(xm) = 0, yields:
% 219.91/170.96  																																	| (1384) all_0_3_3 = xn | xm = sz00 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(all_0_3_3, xm) = v2 & sdtasdt0(xn, xm) = v3 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v3 = v2) &  ~ (all_22_0_25 = all_0_7_7))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (82) with all_22_0_25, all_0_7_7, all_0_3_3, xn, xm and discharging atoms sdtasdt0(xm, all_0_3_3) = all_22_0_25, sdtasdt0(xm, xn) = all_0_7_7, aNaturalNumber0(xm) = 0, yields:
% 219.91/170.96  																																	| (1385) all_0_3_3 = xn | xm = sz00 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(all_0_3_3, xm) = v3 & sdtasdt0(xn, xm) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v3 = v2) &  ~ (all_22_0_25 = all_0_7_7))))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (42) with all_0_7_7, xn yields:
% 219.91/170.96  																																	| (1386)  ~ (sdtasdt0(sz00, xn) = all_0_7_7) |  ? [v0] :  ? [v1] : (sdtasdt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_7_7 = sz00)))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (23) with xp, all_33_2_51, xm, all_99_0_112 and discharging atoms doDivides0(all_99_0_112, xp) = 0, sdtpldt0(xm, all_33_2_51) = xp, yields:
% 219.91/170.96  																																	| (1387)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (doDivides0(all_99_0_112, all_33_2_51) = v4 & doDivides0(all_99_0_112, xm) = v3 & aNaturalNumber0(all_99_0_112) = v0 & aNaturalNumber0(all_33_2_51) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = 0))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (54) with all_0_8_8, xp, all_0_9_9, all_33_2_51, xm and discharging atoms sdtpldt0(xp, all_0_9_9) = all_0_8_8, sdtpldt0(xm, all_33_2_51) = xp, yields:
% 219.91/170.96  																																	| (1388)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (isPrime0(all_0_9_9) = v3 & doDivides0(all_0_9_9, v4) = v5 & doDivides0(all_0_9_9, all_33_2_51) = v8 & doDivides0(all_0_9_9, xm) = v7 & iLess0(all_0_8_8, all_0_8_8) = v6 & sdtasdt0(xm, all_33_2_51) = v4 & aNaturalNumber0(all_33_2_51) = v1 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 219.91/170.96  																																	|
% 219.91/170.96  																																	| Instantiating formula (3) with all_0_8_8, xp, all_0_9_9, all_33_2_51, xm and discharging atoms sdtpldt0(xp, all_0_9_9) = all_0_8_8, sdtpldt0(xm, all_33_2_51) = xp, yields:
% 219.91/170.96  																																	| (1389)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(all_33_2_51, all_0_9_9) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_33_2_51) = v1 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_8_8))
% 219.91/170.96  																																	|
% 219.91/170.97  																																	| Instantiating formula (13) with xp, all_33_2_51, xm and discharging atoms sdtpldt0(xm, all_33_2_51) = xp, yields:
% 219.91/170.97  																																	| (1390)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(all_33_2_51, xm) = v2 & aNaturalNumber0(all_33_2_51) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = xp))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (13) with all_37_1_62, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_37_1_62, yields:
% 219.91/170.97  																																	| (1391)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_37_1_62))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (34) with all_37_1_62, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_37_1_62, yields:
% 219.91/170.97  																																	| (1392)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_37_1_62) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (3) with all_0_8_8, all_0_9_9, xp, xn, xm and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtpldt0(xm, xn) = all_0_9_9, yields:
% 219.91/170.97  																																	| (1393)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(xm, v3) = v4 & sdtpldt0(xn, xp) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_8_8))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (31) with all_0_9_9, all_37_1_62, xn, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_37_1_62, sdtpldt0(xm, xn) = all_0_9_9, yields:
% 219.91/170.97  																																	| (1394) xp = xn |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(xp, xm) = v3 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v4 = v3) &  ~ (all_37_1_62 = all_0_9_9))))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (31) with all_37_1_62, all_0_9_9, xp, xn, xm and discharging atoms sdtpldt0(xm, xp) = all_37_1_62, sdtpldt0(xm, xn) = all_0_9_9, yields:
% 219.91/170.97  																																	| (1395) xp = xn |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(xp, xm) = v4 & sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v4 = v3) &  ~ (all_37_1_62 = all_0_9_9))))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (13) with all_0_8_8, all_37_1_62, xn and discharging atoms sdtpldt0(xn, all_37_1_62) = all_0_8_8, yields:
% 219.91/170.97  																																	| (1396)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(all_37_1_62, xn) = v2 & aNaturalNumber0(all_37_1_62) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = all_0_8_8))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (34) with all_0_8_8, all_37_1_62, xn and discharging atoms sdtpldt0(xn, all_37_1_62) = all_0_8_8, yields:
% 219.91/170.97  																																	| (1397)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_37_1_62) = v1 & aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (23) with xp, all_30_2_42, xn, all_99_0_112 and discharging atoms doDivides0(all_99_0_112, xp) = 0, sdtpldt0(xn, all_30_2_42) = xp, yields:
% 219.91/170.97  																																	| (1398)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (doDivides0(all_99_0_112, all_30_2_42) = v4 & doDivides0(all_99_0_112, xn) = v3 & aNaturalNumber0(all_99_0_112) = v0 & aNaturalNumber0(all_30_2_42) = v2 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = 0))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (54) with all_0_8_8, xp, all_0_9_9, all_30_2_42, xn and discharging atoms sdtpldt0(xp, all_0_9_9) = all_0_8_8, sdtpldt0(xn, all_30_2_42) = xp, yields:
% 219.91/170.97  																																	| (1399)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (isPrime0(all_0_9_9) = v3 & doDivides0(all_0_9_9, v4) = v5 & doDivides0(all_0_9_9, all_30_2_42) = v8 & doDivides0(all_0_9_9, xn) = v7 & iLess0(all_0_8_8, all_0_8_8) = v6 & sdtasdt0(xn, all_30_2_42) = v4 & aNaturalNumber0(all_30_2_42) = v1 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) |  ~ (v5 = 0) |  ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (3) with all_0_8_8, xp, all_0_9_9, all_30_2_42, xn and discharging atoms sdtpldt0(xp, all_0_9_9) = all_0_8_8, sdtpldt0(xn, all_30_2_42) = xp, yields:
% 219.91/170.97  																																	| (1400)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(all_30_2_42, all_0_9_9) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_30_2_42) = v1 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_8_8))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (13) with xp, all_30_2_42, xn and discharging atoms sdtpldt0(xn, all_30_2_42) = xp, yields:
% 219.91/170.97  																																	| (1401)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(all_30_2_42, xn) = v2 & aNaturalNumber0(all_30_2_42) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = xp))
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (92) with all_99_0_112 and discharging atoms aNaturalNumber0(all_99_0_112) = 0, yields:
% 219.91/170.97  																																	| (1402) all_99_0_112 = sz10 | all_99_0_112 = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_99_0_112) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (92) with all_94_0_111 and discharging atoms aNaturalNumber0(all_94_0_111) = 0, yields:
% 219.91/170.97  																																	| (1403) all_94_0_111 = sz10 | all_94_0_111 = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_94_0_111) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (92) with all_34_2_54 and discharging atoms aNaturalNumber0(all_34_2_54) = 0, yields:
% 219.91/170.97  																																	| (1404) all_34_2_54 = sz10 | all_34_2_54 = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_34_2_54) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (92) with all_28_2_36 and discharging atoms aNaturalNumber0(all_28_2_36) = 0, yields:
% 219.91/170.97  																																	| (1405) all_28_2_36 = sz10 | all_28_2_36 = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_28_2_36) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (92) with all_0_3_3 yields:
% 219.91/170.97  																																	| (1406) all_0_3_3 = sz10 | all_0_3_3 = sz00 |  ~ (aNaturalNumber0(all_0_3_3) = 0) |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_0_3_3) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating formula (92) with xk yields:
% 219.91/170.97  																																	| (1407) xk = sz10 | xk = sz00 |  ~ (aNaturalNumber0(xk) = 0) |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating (1401) with all_214_0_113, all_214_1_114, all_214_2_115 yields:
% 219.91/170.97  																																	| (1408) sdtpldt0(all_30_2_42, xn) = all_214_0_113 & aNaturalNumber0(all_30_2_42) = all_214_1_114 & aNaturalNumber0(xn) = all_214_2_115 & ( ~ (all_214_1_114 = 0) |  ~ (all_214_2_115 = 0) | all_214_0_113 = xp)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Applying alpha-rule on (1408) yields:
% 219.91/170.97  																																	| (1409) sdtpldt0(all_30_2_42, xn) = all_214_0_113
% 219.91/170.97  																																	| (1410) aNaturalNumber0(all_30_2_42) = all_214_1_114
% 219.91/170.97  																																	| (1411) aNaturalNumber0(xn) = all_214_2_115
% 219.91/170.97  																																	| (1412)  ~ (all_214_1_114 = 0) |  ~ (all_214_2_115 = 0) | all_214_0_113 = xp
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating (1398) with all_216_0_116, all_216_1_117, all_216_2_118, all_216_3_119, all_216_4_120 yields:
% 219.91/170.97  																																	| (1413) doDivides0(all_99_0_112, all_30_2_42) = all_216_0_116 & doDivides0(all_99_0_112, xn) = all_216_1_117 & aNaturalNumber0(all_99_0_112) = all_216_4_120 & aNaturalNumber0(all_30_2_42) = all_216_2_118 & aNaturalNumber0(xn) = all_216_3_119 & ( ~ (all_216_1_117 = 0) |  ~ (all_216_2_118 = 0) |  ~ (all_216_3_119 = 0) |  ~ (all_216_4_120 = 0) | all_216_0_116 = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Applying alpha-rule on (1413) yields:
% 219.91/170.97  																																	| (1414) aNaturalNumber0(all_99_0_112) = all_216_4_120
% 219.91/170.97  																																	| (1415)  ~ (all_216_1_117 = 0) |  ~ (all_216_2_118 = 0) |  ~ (all_216_3_119 = 0) |  ~ (all_216_4_120 = 0) | all_216_0_116 = 0
% 219.91/170.97  																																	| (1416) doDivides0(all_99_0_112, xn) = all_216_1_117
% 219.91/170.97  																																	| (1417) aNaturalNumber0(all_30_2_42) = all_216_2_118
% 219.91/170.97  																																	| (1418) doDivides0(all_99_0_112, all_30_2_42) = all_216_0_116
% 219.91/170.97  																																	| (1419) aNaturalNumber0(xn) = all_216_3_119
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating (1397) with all_218_0_121, all_218_1_122, all_218_2_123 yields:
% 219.91/170.97  																																	| (1420) aNaturalNumber0(all_37_1_62) = all_218_1_122 & aNaturalNumber0(all_0_8_8) = all_218_0_121 & aNaturalNumber0(xn) = all_218_2_123 & ( ~ (all_218_1_122 = 0) |  ~ (all_218_2_123 = 0) | all_218_0_121 = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Applying alpha-rule on (1420) yields:
% 219.91/170.97  																																	| (1421) aNaturalNumber0(all_37_1_62) = all_218_1_122
% 219.91/170.97  																																	| (1422) aNaturalNumber0(all_0_8_8) = all_218_0_121
% 219.91/170.97  																																	| (1423) aNaturalNumber0(xn) = all_218_2_123
% 219.91/170.97  																																	| (1424)  ~ (all_218_1_122 = 0) |  ~ (all_218_2_123 = 0) | all_218_0_121 = 0
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating (1396) with all_220_0_124, all_220_1_125, all_220_2_126 yields:
% 219.91/170.97  																																	| (1425) sdtpldt0(all_37_1_62, xn) = all_220_0_124 & aNaturalNumber0(all_37_1_62) = all_220_1_125 & aNaturalNumber0(xn) = all_220_2_126 & ( ~ (all_220_1_125 = 0) |  ~ (all_220_2_126 = 0) | all_220_0_124 = all_0_8_8)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Applying alpha-rule on (1425) yields:
% 219.91/170.97  																																	| (1426) sdtpldt0(all_37_1_62, xn) = all_220_0_124
% 219.91/170.97  																																	| (1427) aNaturalNumber0(all_37_1_62) = all_220_1_125
% 219.91/170.97  																																	| (1428) aNaturalNumber0(xn) = all_220_2_126
% 219.91/170.97  																																	| (1429)  ~ (all_220_1_125 = 0) |  ~ (all_220_2_126 = 0) | all_220_0_124 = all_0_8_8
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating (1400) with all_222_0_127, all_222_1_128, all_222_2_129, all_222_3_130, all_222_4_131 yields:
% 219.91/170.97  																																	| (1430) sdtpldt0(all_30_2_42, all_0_9_9) = all_222_1_128 & sdtpldt0(xn, all_222_1_128) = all_222_0_127 & aNaturalNumber0(all_30_2_42) = all_222_3_130 & aNaturalNumber0(all_0_9_9) = all_222_2_129 & aNaturalNumber0(xn) = all_222_4_131 & ( ~ (all_222_2_129 = 0) |  ~ (all_222_3_130 = 0) |  ~ (all_222_4_131 = 0) | all_222_0_127 = all_0_8_8)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Applying alpha-rule on (1430) yields:
% 219.91/170.97  																																	| (1431) aNaturalNumber0(xn) = all_222_4_131
% 219.91/170.97  																																	| (1432) aNaturalNumber0(all_0_9_9) = all_222_2_129
% 219.91/170.97  																																	| (1433)  ~ (all_222_2_129 = 0) |  ~ (all_222_3_130 = 0) |  ~ (all_222_4_131 = 0) | all_222_0_127 = all_0_8_8
% 219.91/170.97  																																	| (1434) sdtpldt0(all_30_2_42, all_0_9_9) = all_222_1_128
% 219.91/170.97  																																	| (1435) sdtpldt0(xn, all_222_1_128) = all_222_0_127
% 219.91/170.97  																																	| (1436) aNaturalNumber0(all_30_2_42) = all_222_3_130
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Instantiating (1399) with all_224_0_132, all_224_1_133, all_224_2_134, all_224_3_135, all_224_4_136, all_224_5_137, all_224_6_138, all_224_7_139, all_224_8_140 yields:
% 219.91/170.97  																																	| (1437) isPrime0(all_0_9_9) = all_224_5_137 & doDivides0(all_0_9_9, all_224_4_136) = all_224_3_135 & doDivides0(all_0_9_9, all_30_2_42) = all_224_0_132 & doDivides0(all_0_9_9, xn) = all_224_1_133 & iLess0(all_0_8_8, all_0_8_8) = all_224_2_134 & sdtasdt0(xn, all_30_2_42) = all_224_4_136 & aNaturalNumber0(all_30_2_42) = all_224_7_139 & aNaturalNumber0(all_0_9_9) = all_224_6_138 & aNaturalNumber0(xn) = all_224_8_140 & ( ~ (all_224_2_134 = 0) |  ~ (all_224_3_135 = 0) |  ~ (all_224_5_137 = 0) |  ~ (all_224_6_138 = 0) |  ~ (all_224_7_139 = 0) |  ~ (all_224_8_140 = 0) | all_224_0_132 = 0 | all_224_1_133 = 0)
% 219.91/170.97  																																	|
% 219.91/170.97  																																	| Applying alpha-rule on (1437) yields:
% 219.91/170.97  																																	| (1438) doDivides0(all_0_9_9, all_224_4_136) = all_224_3_135
% 219.91/170.97  																																	| (1439) aNaturalNumber0(all_30_2_42) = all_224_7_139
% 219.91/170.97  																																	| (1440) sdtasdt0(xn, all_30_2_42) = all_224_4_136
% 219.91/170.97  																																	| (1441)  ~ (all_224_2_134 = 0) |  ~ (all_224_3_135 = 0) |  ~ (all_224_5_137 = 0) |  ~ (all_224_6_138 = 0) |  ~ (all_224_7_139 = 0) |  ~ (all_224_8_140 = 0) | all_224_0_132 = 0 | all_224_1_133 = 0
% 219.91/170.97  																																	| (1442) doDivides0(all_0_9_9, all_30_2_42) = all_224_0_132
% 219.91/170.97  																																	| (1443) isPrime0(all_0_9_9) = all_224_5_137
% 219.91/170.97  																																	| (1444) iLess0(all_0_8_8, all_0_8_8) = all_224_2_134
% 219.91/170.98  																																	| (1445) aNaturalNumber0(all_0_9_9) = all_224_6_138
% 219.91/170.98  																																	| (1446) doDivides0(all_0_9_9, xn) = all_224_1_133
% 219.91/170.98  																																	| (1447) aNaturalNumber0(xn) = all_224_8_140
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1393) with all_226_0_141, all_226_1_142, all_226_2_143, all_226_3_144, all_226_4_145 yields:
% 219.91/170.98  																																	| (1448) sdtpldt0(xm, all_226_1_142) = all_226_0_141 & sdtpldt0(xn, xp) = all_226_1_142 & aNaturalNumber0(xp) = all_226_2_143 & aNaturalNumber0(xm) = all_226_4_145 & aNaturalNumber0(xn) = all_226_3_144 & ( ~ (all_226_2_143 = 0) |  ~ (all_226_3_144 = 0) |  ~ (all_226_4_145 = 0) | all_226_0_141 = all_0_8_8)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1448) yields:
% 219.91/170.98  																																	| (1449) aNaturalNumber0(xp) = all_226_2_143
% 219.91/170.98  																																	| (1450) sdtpldt0(xm, all_226_1_142) = all_226_0_141
% 219.91/170.98  																																	| (1451) aNaturalNumber0(xn) = all_226_3_144
% 219.91/170.98  																																	| (1452)  ~ (all_226_2_143 = 0) |  ~ (all_226_3_144 = 0) |  ~ (all_226_4_145 = 0) | all_226_0_141 = all_0_8_8
% 219.91/170.98  																																	| (1453) aNaturalNumber0(xm) = all_226_4_145
% 219.91/170.98  																																	| (1454) sdtpldt0(xn, xp) = all_226_1_142
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1392) with all_228_0_146, all_228_1_147, all_228_2_148 yields:
% 219.91/170.98  																																	| (1455) aNaturalNumber0(all_37_1_62) = all_228_0_146 & aNaturalNumber0(xp) = all_228_1_147 & aNaturalNumber0(xm) = all_228_2_148 & ( ~ (all_228_1_147 = 0) |  ~ (all_228_2_148 = 0) | all_228_0_146 = 0)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1455) yields:
% 219.91/170.98  																																	| (1456) aNaturalNumber0(all_37_1_62) = all_228_0_146
% 219.91/170.98  																																	| (1457) aNaturalNumber0(xp) = all_228_1_147
% 219.91/170.98  																																	| (1458) aNaturalNumber0(xm) = all_228_2_148
% 219.91/170.98  																																	| (1459)  ~ (all_228_1_147 = 0) |  ~ (all_228_2_148 = 0) | all_228_0_146 = 0
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1391) with all_230_0_149, all_230_1_150, all_230_2_151 yields:
% 219.91/170.98  																																	| (1460) sdtpldt0(xp, xm) = all_230_0_149 & aNaturalNumber0(xp) = all_230_1_150 & aNaturalNumber0(xm) = all_230_2_151 & ( ~ (all_230_1_150 = 0) |  ~ (all_230_2_151 = 0) | all_230_0_149 = all_37_1_62)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1460) yields:
% 219.91/170.98  																																	| (1461) sdtpldt0(xp, xm) = all_230_0_149
% 219.91/170.98  																																	| (1462) aNaturalNumber0(xp) = all_230_1_150
% 219.91/170.98  																																	| (1463) aNaturalNumber0(xm) = all_230_2_151
% 219.91/170.98  																																	| (1464)  ~ (all_230_1_150 = 0) |  ~ (all_230_2_151 = 0) | all_230_0_149 = all_37_1_62
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1390) with all_232_0_152, all_232_1_153, all_232_2_154 yields:
% 219.91/170.98  																																	| (1465) sdtpldt0(all_33_2_51, xm) = all_232_0_152 & aNaturalNumber0(all_33_2_51) = all_232_1_153 & aNaturalNumber0(xm) = all_232_2_154 & ( ~ (all_232_1_153 = 0) |  ~ (all_232_2_154 = 0) | all_232_0_152 = xp)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1465) yields:
% 219.91/170.98  																																	| (1466) sdtpldt0(all_33_2_51, xm) = all_232_0_152
% 219.91/170.98  																																	| (1467) aNaturalNumber0(all_33_2_51) = all_232_1_153
% 219.91/170.98  																																	| (1468) aNaturalNumber0(xm) = all_232_2_154
% 219.91/170.98  																																	| (1469)  ~ (all_232_1_153 = 0) |  ~ (all_232_2_154 = 0) | all_232_0_152 = xp
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1389) with all_234_0_155, all_234_1_156, all_234_2_157, all_234_3_158, all_234_4_159 yields:
% 219.91/170.98  																																	| (1470) sdtpldt0(all_33_2_51, all_0_9_9) = all_234_1_156 & sdtpldt0(xm, all_234_1_156) = all_234_0_155 & aNaturalNumber0(all_33_2_51) = all_234_3_158 & aNaturalNumber0(all_0_9_9) = all_234_2_157 & aNaturalNumber0(xm) = all_234_4_159 & ( ~ (all_234_2_157 = 0) |  ~ (all_234_3_158 = 0) |  ~ (all_234_4_159 = 0) | all_234_0_155 = all_0_8_8)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1470) yields:
% 219.91/170.98  																																	| (1471) aNaturalNumber0(all_33_2_51) = all_234_3_158
% 219.91/170.98  																																	| (1472)  ~ (all_234_2_157 = 0) |  ~ (all_234_3_158 = 0) |  ~ (all_234_4_159 = 0) | all_234_0_155 = all_0_8_8
% 219.91/170.98  																																	| (1473) aNaturalNumber0(xm) = all_234_4_159
% 219.91/170.98  																																	| (1474) sdtpldt0(xm, all_234_1_156) = all_234_0_155
% 219.91/170.98  																																	| (1475) sdtpldt0(all_33_2_51, all_0_9_9) = all_234_1_156
% 219.91/170.98  																																	| (1476) aNaturalNumber0(all_0_9_9) = all_234_2_157
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1382) with all_236_0_160, all_236_1_161, all_236_2_162 yields:
% 219.91/170.98  																																	| (1477) aNaturalNumber0(all_22_0_25) = all_236_0_160 & aNaturalNumber0(all_0_3_3) = all_236_1_161 & aNaturalNumber0(xm) = all_236_2_162 & ( ~ (all_236_1_161 = 0) |  ~ (all_236_2_162 = 0) | all_236_0_160 = 0)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1477) yields:
% 219.91/170.98  																																	| (1478) aNaturalNumber0(all_22_0_25) = all_236_0_160
% 219.91/170.98  																																	| (1479) aNaturalNumber0(all_0_3_3) = all_236_1_161
% 219.91/170.98  																																	| (1480) aNaturalNumber0(xm) = all_236_2_162
% 219.91/170.98  																																	| (1481)  ~ (all_236_1_161 = 0) |  ~ (all_236_2_162 = 0) | all_236_0_160 = 0
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1388) with all_238_0_163, all_238_1_164, all_238_2_165, all_238_3_166, all_238_4_167, all_238_5_168, all_238_6_169, all_238_7_170, all_238_8_171 yields:
% 219.91/170.98  																																	| (1482) isPrime0(all_0_9_9) = all_238_5_168 & doDivides0(all_0_9_9, all_238_4_167) = all_238_3_166 & doDivides0(all_0_9_9, all_33_2_51) = all_238_0_163 & doDivides0(all_0_9_9, xm) = all_238_1_164 & iLess0(all_0_8_8, all_0_8_8) = all_238_2_165 & sdtasdt0(xm, all_33_2_51) = all_238_4_167 & aNaturalNumber0(all_33_2_51) = all_238_7_170 & aNaturalNumber0(all_0_9_9) = all_238_6_169 & aNaturalNumber0(xm) = all_238_8_171 & ( ~ (all_238_2_165 = 0) |  ~ (all_238_3_166 = 0) |  ~ (all_238_5_168 = 0) |  ~ (all_238_6_169 = 0) |  ~ (all_238_7_170 = 0) |  ~ (all_238_8_171 = 0) | all_238_0_163 = 0 | all_238_1_164 = 0)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1482) yields:
% 219.91/170.98  																																	| (1483) aNaturalNumber0(all_33_2_51) = all_238_7_170
% 219.91/170.98  																																	| (1484) aNaturalNumber0(xm) = all_238_8_171
% 219.91/170.98  																																	| (1485) iLess0(all_0_8_8, all_0_8_8) = all_238_2_165
% 219.91/170.98  																																	| (1486) doDivides0(all_0_9_9, all_33_2_51) = all_238_0_163
% 219.91/170.98  																																	| (1487) sdtasdt0(xm, all_33_2_51) = all_238_4_167
% 219.91/170.98  																																	| (1488) isPrime0(all_0_9_9) = all_238_5_168
% 219.91/170.98  																																	| (1489) aNaturalNumber0(all_0_9_9) = all_238_6_169
% 219.91/170.98  																																	| (1490)  ~ (all_238_2_165 = 0) |  ~ (all_238_3_166 = 0) |  ~ (all_238_5_168 = 0) |  ~ (all_238_6_169 = 0) |  ~ (all_238_7_170 = 0) |  ~ (all_238_8_171 = 0) | all_238_0_163 = 0 | all_238_1_164 = 0
% 219.91/170.98  																																	| (1491) doDivides0(all_0_9_9, xm) = all_238_1_164
% 219.91/170.98  																																	| (1492) doDivides0(all_0_9_9, all_238_4_167) = all_238_3_166
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1387) with all_240_0_172, all_240_1_173, all_240_2_174, all_240_3_175, all_240_4_176 yields:
% 219.91/170.98  																																	| (1493) doDivides0(all_99_0_112, all_33_2_51) = all_240_0_172 & doDivides0(all_99_0_112, xm) = all_240_1_173 & aNaturalNumber0(all_99_0_112) = all_240_4_176 & aNaturalNumber0(all_33_2_51) = all_240_2_174 & aNaturalNumber0(xm) = all_240_3_175 & ( ~ (all_240_1_173 = 0) |  ~ (all_240_2_174 = 0) |  ~ (all_240_3_175 = 0) |  ~ (all_240_4_176 = 0) | all_240_0_172 = 0)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1493) yields:
% 219.91/170.98  																																	| (1494) aNaturalNumber0(all_99_0_112) = all_240_4_176
% 219.91/170.98  																																	| (1495) aNaturalNumber0(xm) = all_240_3_175
% 219.91/170.98  																																	| (1496) doDivides0(all_99_0_112, all_33_2_51) = all_240_0_172
% 219.91/170.98  																																	| (1497)  ~ (all_240_1_173 = 0) |  ~ (all_240_2_174 = 0) |  ~ (all_240_3_175 = 0) |  ~ (all_240_4_176 = 0) | all_240_0_172 = 0
% 219.91/170.98  																																	| (1498) doDivides0(all_99_0_112, xm) = all_240_1_173
% 219.91/170.98  																																	| (1499) aNaturalNumber0(all_33_2_51) = all_240_2_174
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1374) with all_242_0_177, all_242_1_178, all_242_2_179 yields:
% 219.91/170.98  																																	| (1500) sdtasdt0(all_34_2_54, xr) = all_242_0_177 & aNaturalNumber0(all_34_2_54) = all_242_1_178 & aNaturalNumber0(xr) = all_242_2_179 & ( ~ (all_242_1_178 = 0) |  ~ (all_242_2_179 = 0) | all_242_0_177 = xn)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1500) yields:
% 219.91/170.98  																																	| (1501) sdtasdt0(all_34_2_54, xr) = all_242_0_177
% 219.91/170.98  																																	| (1502) aNaturalNumber0(all_34_2_54) = all_242_1_178
% 219.91/170.98  																																	| (1503) aNaturalNumber0(xr) = all_242_2_179
% 219.91/170.98  																																	| (1504)  ~ (all_242_1_178 = 0) |  ~ (all_242_2_179 = 0) | all_242_0_177 = xn
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1373) with all_244_0_180, all_244_1_181, all_244_2_182, all_244_3_183, all_244_4_184 yields:
% 219.91/170.98  																																	| (1505) sdtasdt0(all_34_2_54, xm) = all_244_1_181 & sdtasdt0(xr, all_244_1_181) = all_244_0_180 & aNaturalNumber0(all_34_2_54) = all_244_3_183 & aNaturalNumber0(xr) = all_244_4_184 & aNaturalNumber0(xm) = all_244_2_182 & ( ~ (all_244_2_182 = 0) |  ~ (all_244_3_183 = 0) |  ~ (all_244_4_184 = 0) | all_244_0_180 = all_0_7_7)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1505) yields:
% 219.91/170.98  																																	| (1506) sdtasdt0(all_34_2_54, xm) = all_244_1_181
% 219.91/170.98  																																	| (1507) aNaturalNumber0(all_34_2_54) = all_244_3_183
% 219.91/170.98  																																	| (1508) aNaturalNumber0(xr) = all_244_4_184
% 219.91/170.98  																																	| (1509)  ~ (all_244_2_182 = 0) |  ~ (all_244_3_183 = 0) |  ~ (all_244_4_184 = 0) | all_244_0_180 = all_0_7_7
% 219.91/170.98  																																	| (1510) sdtasdt0(xr, all_244_1_181) = all_244_0_180
% 219.91/170.98  																																	| (1511) aNaturalNumber0(xm) = all_244_2_182
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1371) with all_246_0_185, all_246_1_186, all_246_2_187 yields:
% 219.91/170.98  																																	| (1512) sdtasdt0(all_41_2_77, xr) = all_246_0_185 & aNaturalNumber0(all_41_2_77) = all_246_1_186 & aNaturalNumber0(xr) = all_246_2_187 & ( ~ (all_246_1_186 = 0) |  ~ (all_246_2_187 = 0) | all_246_0_185 = all_0_7_7)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1512) yields:
% 219.91/170.98  																																	| (1513) sdtasdt0(all_41_2_77, xr) = all_246_0_185
% 219.91/170.98  																																	| (1514) aNaturalNumber0(all_41_2_77) = all_246_1_186
% 219.91/170.98  																																	| (1515) aNaturalNumber0(xr) = all_246_2_187
% 219.91/170.98  																																	| (1516)  ~ (all_246_1_186 = 0) |  ~ (all_246_2_187 = 0) | all_246_0_185 = all_0_7_7
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1363) with all_249_0_191, all_249_1_192, all_249_2_193 yields:
% 219.91/170.98  																																	| (1517) (all_249_0_191 = xp & all_249_1_192 = 0 & sdtasdt0(all_99_0_112, all_249_2_193) = xp & aNaturalNumber0(all_249_2_193) = 0) | (aNaturalNumber0(all_99_0_112) = all_249_2_193 & aNaturalNumber0(xp) = all_249_1_192 & ( ~ (all_249_1_192 = 0) |  ~ (all_249_2_193 = 0)))
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Instantiating (1381) with all_250_0_194, all_250_1_195, all_250_2_196 yields:
% 219.91/170.98  																																	| (1518) sdtasdt0(all_0_3_3, xm) = all_250_0_194 & aNaturalNumber0(all_0_3_3) = all_250_1_195 & aNaturalNumber0(xm) = all_250_2_196 & ( ~ (all_250_1_195 = 0) |  ~ (all_250_2_196 = 0) | all_250_0_194 = all_22_0_25)
% 219.91/170.98  																																	|
% 219.91/170.98  																																	| Applying alpha-rule on (1518) yields:
% 219.91/170.98  																																	| (1519) sdtasdt0(all_0_3_3, xm) = all_250_0_194
% 219.91/170.98  																																	| (1520) aNaturalNumber0(all_0_3_3) = all_250_1_195
% 219.91/170.98  																																	| (1521) aNaturalNumber0(xm) = all_250_2_196
% 219.91/170.98  																																	| (1522)  ~ (all_250_1_195 = 0) |  ~ (all_250_2_196 = 0) | all_250_0_194 = all_22_0_25
% 219.91/170.99  																																	|
% 219.91/170.99  																																	| Instantiating (1379) with all_252_0_197, all_252_1_198, all_252_2_199 yields:
% 219.91/170.99  																																	| (1523) sdtasdt0(all_28_2_36, xp) = all_252_0_197 & aNaturalNumber0(all_28_2_36) = all_252_1_198 & aNaturalNumber0(xp) = all_252_2_199 & ( ~ (all_252_1_198 = 0) |  ~ (all_252_2_199 = 0) | all_252_0_197 = all_0_7_7)
% 219.91/170.99  																																	|
% 219.91/170.99  																																	| Applying alpha-rule on (1523) yields:
% 219.91/170.99  																																	| (1524) sdtasdt0(all_28_2_36, xp) = all_252_0_197
% 219.91/170.99  																																	| (1525) aNaturalNumber0(all_28_2_36) = all_252_1_198
% 219.91/170.99  																																	| (1526) aNaturalNumber0(xp) = all_252_2_199
% 219.91/170.99  																																	| (1527)  ~ (all_252_1_198 = 0) |  ~ (all_252_2_199 = 0) | all_252_0_197 = all_0_7_7
% 219.91/170.99  																																	|
% 219.91/170.99  																																	+-Applying beta-rule and splitting (1403), into two cases.
% 219.91/170.99  																																	|-Branch one:
% 219.91/170.99  																																	| (1528) all_94_0_111 = sz00
% 219.91/170.99  																																	|
% 219.91/170.99  																																		| Equations (1528) can reduce 301 to:
% 219.91/170.99  																																		| (197) $false
% 219.91/170.99  																																		|
% 219.91/170.99  																																		|-The branch is then unsatisfiable
% 219.91/170.99  																																	|-Branch two:
% 219.91/170.99  																																	| (301)  ~ (all_94_0_111 = sz00)
% 219.91/170.99  																																	| (1531) all_94_0_111 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_94_0_111) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.99  																																	|
% 219.91/170.99  																																		+-Applying beta-rule and splitting (1402), into two cases.
% 219.91/170.99  																																		|-Branch one:
% 219.91/170.99  																																		| (1532) all_99_0_112 = sz00
% 219.91/170.99  																																		|
% 219.91/170.99  																																			| Equations (1532) can reduce 299 to:
% 219.91/170.99  																																			| (197) $false
% 219.91/170.99  																																			|
% 219.91/170.99  																																			|-The branch is then unsatisfiable
% 219.91/170.99  																																		|-Branch two:
% 219.91/170.99  																																		| (299)  ~ (all_99_0_112 = sz00)
% 219.91/170.99  																																		| (1535) all_99_0_112 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_99_0_112) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.99  																																		|
% 219.91/170.99  																																			+-Applying beta-rule and splitting (1531), into two cases.
% 219.91/170.99  																																			|-Branch one:
% 219.91/170.99  																																			| (1536) all_94_0_111 = sz10
% 219.91/170.99  																																			|
% 219.91/170.99  																																				| Equations (1536) can reduce 300 to:
% 219.91/170.99  																																				| (197) $false
% 219.91/170.99  																																				|
% 219.91/170.99  																																				|-The branch is then unsatisfiable
% 219.91/170.99  																																			|-Branch two:
% 219.91/170.99  																																			| (300)  ~ (all_94_0_111 = sz10)
% 219.91/170.99  																																			| (1539)  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_94_0_111) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.99  																																			|
% 219.91/170.99  																																				+-Applying beta-rule and splitting (1535), into two cases.
% 219.91/170.99  																																				|-Branch one:
% 219.91/170.99  																																				| (1540) all_99_0_112 = sz10
% 219.91/170.99  																																				|
% 219.91/170.99  																																					| Equations (1540) can reduce 298 to:
% 219.91/170.99  																																					| (197) $false
% 219.91/170.99  																																					|
% 219.91/170.99  																																					|-The branch is then unsatisfiable
% 219.91/170.99  																																				|-Branch two:
% 219.91/170.99  																																				| (298)  ~ (all_99_0_112 = sz10)
% 219.91/170.99  																																				| (1543)  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_99_0_112) = 0 & aNaturalNumber0(v0) = 0)
% 219.91/170.99  																																				|
% 219.91/170.99  																																					| Instantiating formula (49) with all_0_3_3, xm, all_244_1_181, all_0_2_2 and discharging atoms sdtasdt0(all_0_3_3, xm) = all_0_2_2, yields:
% 219.91/170.99  																																					| (1544) all_244_1_181 = all_0_2_2 |  ~ (sdtasdt0(all_0_3_3, xm) = all_244_1_181)
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (49) with xr, all_34_2_54, all_244_0_180, xn and discharging atoms sdtasdt0(xr, all_34_2_54) = xn, yields:
% 219.91/170.99  																																					| (1545) all_244_0_180 = xn |  ~ (sdtasdt0(xr, all_34_2_54) = all_244_0_180)
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_99_0_112, all_240_4_176, 0 and discharging atoms aNaturalNumber0(all_99_0_112) = all_240_4_176, aNaturalNumber0(all_99_0_112) = 0, yields:
% 219.91/170.99  																																					| (1546) all_240_4_176 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_99_0_112, all_216_4_120, all_240_4_176 and discharging atoms aNaturalNumber0(all_99_0_112) = all_240_4_176, aNaturalNumber0(all_99_0_112) = all_216_4_120, yields:
% 219.91/170.99  																																					| (1547) all_240_4_176 = all_216_4_120
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_34_2_54, all_244_3_183, 0 and discharging atoms aNaturalNumber0(all_34_2_54) = all_244_3_183, aNaturalNumber0(all_34_2_54) = 0, yields:
% 219.91/170.99  																																					| (1548) all_244_3_183 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_34_2_54, all_242_1_178, all_244_3_183 and discharging atoms aNaturalNumber0(all_34_2_54) = all_244_3_183, aNaturalNumber0(all_34_2_54) = all_242_1_178, yields:
% 219.91/170.99  																																					| (1549) all_244_3_183 = all_242_1_178
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_30_2_42, all_224_7_139, 0 and discharging atoms aNaturalNumber0(all_30_2_42) = all_224_7_139, aNaturalNumber0(all_30_2_42) = 0, yields:
% 219.91/170.99  																																					| (1550) all_224_7_139 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_30_2_42, all_222_3_130, all_224_7_139 and discharging atoms aNaturalNumber0(all_30_2_42) = all_224_7_139, aNaturalNumber0(all_30_2_42) = all_222_3_130, yields:
% 219.91/170.99  																																					| (1551) all_224_7_139 = all_222_3_130
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_30_2_42, all_216_2_118, all_222_3_130 and discharging atoms aNaturalNumber0(all_30_2_42) = all_222_3_130, aNaturalNumber0(all_30_2_42) = all_216_2_118, yields:
% 219.91/170.99  																																					| (1552) all_222_3_130 = all_216_2_118
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_28_2_36, all_252_1_198, 0 and discharging atoms aNaturalNumber0(all_28_2_36) = all_252_1_198, aNaturalNumber0(all_28_2_36) = 0, yields:
% 219.91/170.99  																																					| (1553) all_252_1_198 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_2_2, all_236_0_160, all_20_0_22 and discharging atoms aNaturalNumber0(all_0_2_2) = all_20_0_22, yields:
% 219.91/170.99  																																					| (1554) all_236_0_160 = all_20_0_22 |  ~ (aNaturalNumber0(all_0_2_2) = all_236_0_160)
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_3_3, all_250_1_195, all_20_2_24 and discharging atoms aNaturalNumber0(all_0_3_3) = all_250_1_195, aNaturalNumber0(all_0_3_3) = all_20_2_24, yields:
% 219.91/170.99  																																					| (1555) all_250_1_195 = all_20_2_24
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_3_3, all_250_1_195, all_216_2_118 and discharging atoms aNaturalNumber0(all_0_3_3) = all_250_1_195, yields:
% 219.91/170.99  																																					| (1556) all_250_1_195 = all_216_2_118 |  ~ (aNaturalNumber0(all_0_3_3) = all_216_2_118)
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_3_3, all_236_1_161, all_250_1_195 and discharging atoms aNaturalNumber0(all_0_3_3) = all_250_1_195, aNaturalNumber0(all_0_3_3) = all_236_1_161, yields:
% 219.91/170.99  																																					| (1557) all_250_1_195 = all_236_1_161
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_8_8, all_218_0_121, 0 and discharging atoms aNaturalNumber0(all_0_8_8) = all_218_0_121, aNaturalNumber0(all_0_8_8) = 0, yields:
% 219.91/170.99  																																					| (1558) all_218_0_121 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_9_9, all_234_2_157, all_238_6_169 and discharging atoms aNaturalNumber0(all_0_9_9) = all_238_6_169, aNaturalNumber0(all_0_9_9) = all_234_2_157, yields:
% 219.91/170.99  																																					| (1559) all_238_6_169 = all_234_2_157
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_9_9, all_224_6_138, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_224_6_138, aNaturalNumber0(all_0_9_9) = 0, yields:
% 219.91/170.99  																																					| (1560) all_224_6_138 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_9_9, all_224_6_138, all_234_2_157 and discharging atoms aNaturalNumber0(all_0_9_9) = all_234_2_157, aNaturalNumber0(all_0_9_9) = all_224_6_138, yields:
% 219.91/170.99  																																					| (1561) all_234_2_157 = all_224_6_138
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with all_0_9_9, all_222_2_129, all_238_6_169 and discharging atoms aNaturalNumber0(all_0_9_9) = all_238_6_169, aNaturalNumber0(all_0_9_9) = all_222_2_129, yields:
% 219.91/170.99  																																					| (1562) all_238_6_169 = all_222_2_129
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xr, all_246_2_187, 0 and discharging atoms aNaturalNumber0(xr) = all_246_2_187, aNaturalNumber0(xr) = 0, yields:
% 219.91/170.99  																																					| (1563) all_246_2_187 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xr, all_244_4_184, all_246_2_187 and discharging atoms aNaturalNumber0(xr) = all_246_2_187, aNaturalNumber0(xr) = all_244_4_184, yields:
% 219.91/170.99  																																					| (1564) all_246_2_187 = all_244_4_184
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xr, all_242_2_179, all_244_4_184 and discharging atoms aNaturalNumber0(xr) = all_244_4_184, aNaturalNumber0(xr) = all_242_2_179, yields:
% 219.91/170.99  																																					| (1565) all_244_4_184 = all_242_2_179
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xp, all_252_2_199, 0 and discharging atoms aNaturalNumber0(xp) = all_252_2_199, aNaturalNumber0(xp) = 0, yields:
% 219.91/170.99  																																					| (1566) all_252_2_199 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xp, all_230_1_150, all_252_2_199 and discharging atoms aNaturalNumber0(xp) = all_252_2_199, aNaturalNumber0(xp) = all_230_1_150, yields:
% 219.91/170.99  																																					| (1567) all_252_2_199 = all_230_1_150
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xp, all_228_1_147, all_230_1_150 and discharging atoms aNaturalNumber0(xp) = all_230_1_150, aNaturalNumber0(xp) = all_228_1_147, yields:
% 219.91/170.99  																																					| (1568) all_230_1_150 = all_228_1_147
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xp, all_226_2_143, all_228_1_147 and discharging atoms aNaturalNumber0(xp) = all_228_1_147, aNaturalNumber0(xp) = all_226_2_143, yields:
% 219.91/170.99  																																					| (1569) all_228_1_147 = all_226_2_143
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_244_2_182, all_250_2_196 and discharging atoms aNaturalNumber0(xm) = all_250_2_196, aNaturalNumber0(xm) = all_244_2_182, yields:
% 219.91/170.99  																																					| (1570) all_250_2_196 = all_244_2_182
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_238_8_171, all_240_3_175 and discharging atoms aNaturalNumber0(xm) = all_240_3_175, aNaturalNumber0(xm) = all_238_8_171, yields:
% 219.91/170.99  																																					| (1571) all_240_3_175 = all_238_8_171
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_236_2_162, all_250_2_196 and discharging atoms aNaturalNumber0(xm) = all_250_2_196, aNaturalNumber0(xm) = all_236_2_162, yields:
% 219.91/170.99  																																					| (1572) all_250_2_196 = all_236_2_162
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_236_2_162, all_238_8_171 and discharging atoms aNaturalNumber0(xm) = all_238_8_171, aNaturalNumber0(xm) = all_236_2_162, yields:
% 219.91/170.99  																																					| (1573) all_238_8_171 = all_236_2_162
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_232_2_154, 0 and discharging atoms aNaturalNumber0(xm) = all_232_2_154, aNaturalNumber0(xm) = 0, yields:
% 219.91/170.99  																																					| (1574) all_232_2_154 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_232_2_154, all_250_2_196 and discharging atoms aNaturalNumber0(xm) = all_250_2_196, aNaturalNumber0(xm) = all_232_2_154, yields:
% 219.91/170.99  																																					| (1575) all_250_2_196 = all_232_2_154
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_232_2_154, all_234_4_159 and discharging atoms aNaturalNumber0(xm) = all_234_4_159, aNaturalNumber0(xm) = all_232_2_154, yields:
% 219.91/170.99  																																					| (1576) all_234_4_159 = all_232_2_154
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_230_2_151, all_250_2_196 and discharging atoms aNaturalNumber0(xm) = all_250_2_196, aNaturalNumber0(xm) = all_230_2_151, yields:
% 219.91/170.99  																																					| (1577) all_250_2_196 = all_230_2_151
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_228_2_148, all_234_4_159 and discharging atoms aNaturalNumber0(xm) = all_234_4_159, aNaturalNumber0(xm) = all_228_2_148, yields:
% 219.91/170.99  																																					| (1578) all_234_4_159 = all_228_2_148
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xm, all_226_4_145, all_240_3_175 and discharging atoms aNaturalNumber0(xm) = all_240_3_175, aNaturalNumber0(xm) = all_226_4_145, yields:
% 219.91/170.99  																																					| (1579) all_240_3_175 = all_226_4_145
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_224_8_140, 0 and discharging atoms aNaturalNumber0(xn) = all_224_8_140, aNaturalNumber0(xn) = 0, yields:
% 219.91/170.99  																																					| (1580) all_224_8_140 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_222_4_131, all_226_3_144 and discharging atoms aNaturalNumber0(xn) = all_226_3_144, aNaturalNumber0(xn) = all_222_4_131, yields:
% 219.91/170.99  																																					| (1581) all_226_3_144 = all_222_4_131
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_222_4_131, all_224_8_140 and discharging atoms aNaturalNumber0(xn) = all_224_8_140, aNaturalNumber0(xn) = all_222_4_131, yields:
% 219.91/170.99  																																					| (1582) all_224_8_140 = all_222_4_131
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_220_2_126, all_222_4_131 and discharging atoms aNaturalNumber0(xn) = all_222_4_131, aNaturalNumber0(xn) = all_220_2_126, yields:
% 219.91/170.99  																																					| (1583) all_222_4_131 = all_220_2_126
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_218_2_123, all_224_8_140 and discharging atoms aNaturalNumber0(xn) = all_224_8_140, aNaturalNumber0(xn) = all_218_2_123, yields:
% 219.91/170.99  																																					| (1584) all_224_8_140 = all_218_2_123
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_216_3_119, all_226_3_144 and discharging atoms aNaturalNumber0(xn) = all_226_3_144, aNaturalNumber0(xn) = all_216_3_119, yields:
% 219.91/170.99  																																					| (1585) all_226_3_144 = all_216_3_119
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Instantiating formula (28) with xn, all_214_2_115, all_224_8_140 and discharging atoms aNaturalNumber0(xn) = all_224_8_140, aNaturalNumber0(xn) = all_214_2_115, yields:
% 219.91/170.99  																																					| (1586) all_224_8_140 = all_214_2_115
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1567,1566) yields a new equation:
% 219.91/170.99  																																					| (1587) all_230_1_150 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Simplifying 1587 yields:
% 219.91/170.99  																																					| (1588) all_230_1_150 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1555,1557) yields a new equation:
% 219.91/170.99  																																					| (1589) all_236_1_161 = all_20_2_24
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1575,1570) yields a new equation:
% 219.91/170.99  																																					| (1590) all_244_2_182 = all_232_2_154
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1572,1570) yields a new equation:
% 219.91/170.99  																																					| (1591) all_244_2_182 = all_236_2_162
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1577,1570) yields a new equation:
% 219.91/170.99  																																					| (1592) all_244_2_182 = all_230_2_151
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1564,1563) yields a new equation:
% 219.91/170.99  																																					| (1593) all_244_4_184 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Simplifying 1593 yields:
% 219.91/170.99  																																					| (1594) all_244_4_184 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1590,1592) yields a new equation:
% 219.91/170.99  																																					| (1595) all_232_2_154 = all_230_2_151
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Simplifying 1595 yields:
% 219.91/170.99  																																					| (1596) all_232_2_154 = all_230_2_151
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1591,1592) yields a new equation:
% 219.91/170.99  																																					| (1597) all_236_2_162 = all_230_2_151
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Simplifying 1597 yields:
% 219.91/170.99  																																					| (1598) all_236_2_162 = all_230_2_151
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1548,1549) yields a new equation:
% 219.91/170.99  																																					| (1599) all_242_1_178 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1565,1594) yields a new equation:
% 219.91/170.99  																																					| (1600) all_242_2_179 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Simplifying 1600 yields:
% 219.91/170.99  																																					| (1601) all_242_2_179 = 0
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1571,1579) yields a new equation:
% 219.91/170.99  																																					| (1602) all_238_8_171 = all_226_4_145
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Simplifying 1602 yields:
% 219.91/170.99  																																					| (1603) all_238_8_171 = all_226_4_145
% 219.91/170.99  																																					|
% 219.91/170.99  																																					| Combining equations (1547,1546) yields a new equation:
% 219.91/170.99  																																					| (1604) all_216_4_120 = 0
% 219.91/170.99  																																					|
% 219.91/171.00  																																					| Simplifying 1604 yields:
% 219.91/171.00  																																					| (1605) all_216_4_120 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1559,1562) yields a new equation:
% 219.91/171.00  																																					| (1606) all_234_2_157 = all_222_2_129
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1606 yields:
% 219.91/171.00  																																					| (1607) all_234_2_157 = all_222_2_129
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1573,1603) yields a new equation:
% 219.91/171.00  																																					| (1608) all_236_2_162 = all_226_4_145
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1608 yields:
% 219.91/171.00  																																					| (1609) all_236_2_162 = all_226_4_145
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1598,1609) yields a new equation:
% 219.91/171.00  																																					| (1610) all_230_2_151 = all_226_4_145
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1610 yields:
% 219.91/171.00  																																					| (1611) all_230_2_151 = all_226_4_145
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1561,1607) yields a new equation:
% 219.91/171.00  																																					| (1612) all_224_6_138 = all_222_2_129
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1612 yields:
% 219.91/171.00  																																					| (1613) all_224_6_138 = all_222_2_129
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1576,1578) yields a new equation:
% 219.91/171.00  																																					| (1614) all_232_2_154 = all_228_2_148
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1614 yields:
% 219.91/171.00  																																					| (1615) all_232_2_154 = all_228_2_148
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1574,1615) yields a new equation:
% 219.91/171.00  																																					| (1616) all_228_2_148 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1596,1615) yields a new equation:
% 219.91/171.00  																																					| (1617) all_230_2_151 = all_228_2_148
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1617 yields:
% 219.91/171.00  																																					| (1618) all_230_2_151 = all_228_2_148
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1568,1588) yields a new equation:
% 219.91/171.00  																																					| (1619) all_228_1_147 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1619 yields:
% 219.91/171.00  																																					| (1620) all_228_1_147 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1618,1611) yields a new equation:
% 219.91/171.00  																																					| (1621) all_228_2_148 = all_226_4_145
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1621 yields:
% 219.91/171.00  																																					| (1622) all_228_2_148 = all_226_4_145
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1569,1620) yields a new equation:
% 219.91/171.00  																																					| (1623) all_226_2_143 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1623 yields:
% 219.91/171.00  																																					| (1624) all_226_2_143 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1616,1622) yields a new equation:
% 219.91/171.00  																																					| (1625) all_226_4_145 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1581,1585) yields a new equation:
% 219.91/171.00  																																					| (1626) all_222_4_131 = all_216_3_119
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1626 yields:
% 219.91/171.00  																																					| (1627) all_222_4_131 = all_216_3_119
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1613,1560) yields a new equation:
% 219.91/171.00  																																					| (1628) all_222_2_129 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1628 yields:
% 219.91/171.00  																																					| (1629) all_222_2_129 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1551,1550) yields a new equation:
% 219.91/171.00  																																					| (1630) all_222_3_130 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1630 yields:
% 219.91/171.00  																																					| (1631) all_222_3_130 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1580,1584) yields a new equation:
% 219.91/171.00  																																					| (1632) all_218_2_123 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1586,1584) yields a new equation:
% 219.91/171.00  																																					| (1633) all_218_2_123 = all_214_2_115
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1582,1584) yields a new equation:
% 219.91/171.00  																																					| (1634) all_222_4_131 = all_218_2_123
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1634 yields:
% 219.91/171.00  																																					| (1635) all_222_4_131 = all_218_2_123
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1552,1631) yields a new equation:
% 219.91/171.00  																																					| (1636) all_216_2_118 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1636 yields:
% 219.91/171.00  																																					| (1637) all_216_2_118 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1627,1583) yields a new equation:
% 219.91/171.00  																																					| (1638) all_220_2_126 = all_216_3_119
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1635,1583) yields a new equation:
% 219.91/171.00  																																					| (1639) all_220_2_126 = all_218_2_123
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1639,1638) yields a new equation:
% 219.91/171.00  																																					| (1640) all_218_2_123 = all_216_3_119
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Simplifying 1640 yields:
% 219.91/171.00  																																					| (1641) all_218_2_123 = all_216_3_119
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1632,1641) yields a new equation:
% 219.91/171.00  																																					| (1642) all_216_3_119 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1633,1641) yields a new equation:
% 219.91/171.00  																																					| (1643) all_216_3_119 = all_214_2_115
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1642,1643) yields a new equation:
% 219.91/171.00  																																					| (1644) all_214_2_115 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1625,1611) yields a new equation:
% 219.91/171.00  																																					| (1645) all_230_2_151 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1599,1549) yields a new equation:
% 219.91/171.00  																																					| (1548) all_244_3_183 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1645,1592) yields a new equation:
% 219.91/171.00  																																					| (1647) all_244_2_182 = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| Combining equations (1589,1557) yields a new equation:
% 219.91/171.00  																																					| (1555) all_250_1_195 = all_20_2_24
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1605) and (1414) follows:
% 219.91/171.00  																																					| (297) aNaturalNumber0(all_99_0_112) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1599) and (1502) follows:
% 219.91/171.00  																																					| (1342) aNaturalNumber0(all_34_2_54) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1553) and (1525) follows:
% 219.91/171.00  																																					| (1305) aNaturalNumber0(all_28_2_36) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1589) and (1479) follows:
% 219.91/171.00  																																					| (154) aNaturalNumber0(all_0_3_3) = all_20_2_24
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1558) and (1422) follows:
% 219.91/171.00  																																					| (1351) aNaturalNumber0(all_0_8_8) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1629) and (1432) follows:
% 219.91/171.00  																																					| (1284) aNaturalNumber0(all_0_9_9) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1601) and (1503) follows:
% 219.91/171.00  																																					| (88) aNaturalNumber0(xr) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1624) and (1449) follows:
% 219.91/171.00  																																					| (9) aNaturalNumber0(xp) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1625) and (1453) follows:
% 219.91/171.00  																																					| (12) aNaturalNumber0(xm) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					| From (1644) and (1411) follows:
% 219.91/171.00  																																					| (91) aNaturalNumber0(xn) = 0
% 219.91/171.00  																																					|
% 219.91/171.00  																																					+-Applying beta-rule and splitting (1376), into two cases.
% 219.91/171.00  																																					|-Branch one:
% 219.91/171.00  																																					| (278) xp = sz00
% 219.91/171.00  																																					|
% 219.91/171.00  																																						| Equations (278) can reduce 101 to:
% 219.91/171.00  																																						| (197) $false
% 219.91/171.00  																																						|
% 219.91/171.00  																																						|-The branch is then unsatisfiable
% 219.91/171.00  																																					|-Branch two:
% 219.91/171.00  																																					| (101)  ~ (xp = sz00)
% 219.91/171.00  																																					| (1662) all_28_2_36 = xk |  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_28_2_36) = v0) | (doDivides0(xp, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))))
% 219.91/171.00  																																					|
% 219.91/171.00  																																						+-Applying beta-rule and splitting (1662), into two cases.
% 219.91/171.00  																																						|-Branch one:
% 219.91/171.00  																																						| (1663) all_28_2_36 = xk
% 219.91/171.00  																																						|
% 219.91/171.00  																																							| From (1663) and (1304) follows:
% 219.91/171.00  																																							| (1664) sdtasdt0(xp, xk) = all_0_7_7
% 219.91/171.00  																																							|
% 219.91/171.00  																																							| From (1663) and (1305) follows:
% 219.91/171.00  																																							| (1665) aNaturalNumber0(xk) = 0
% 219.91/171.00  																																							|
% 219.91/171.00  																																							+-Applying beta-rule and splitting (1364), into two cases.
% 219.91/171.00  																																							|-Branch one:
% 219.91/171.00  																																							| (1666) all_94_0_111 = xr
% 219.91/171.00  																																							|
% 219.91/171.00  																																								| Equations (1666) can reduce 301 to:
% 219.91/171.00  																																								| (100)  ~ (xr = sz00)
% 219.91/171.00  																																								|
% 219.91/171.00  																																								| From (1666) and (289) follows:
% 219.91/171.00  																																								| (88) aNaturalNumber0(xr) = 0
% 219.91/171.00  																																								|
% 219.91/171.00  																																								+-Applying beta-rule and splitting (518), into two cases.
% 219.91/171.00  																																								|-Branch one:
% 219.91/171.00  																																								| (1669)  ~ (aNaturalNumber0(xk) = all_12_0_10)
% 219.91/171.00  																																								|
% 219.91/171.00  																																									| From (1281) and (1669) follows:
% 219.91/171.00  																																									| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 219.91/171.00  																																									|
% 219.91/171.00  																																									| Using (1665) and (1670) yields:
% 219.91/171.00  																																									| (1311) $false
% 219.91/171.00  																																									|
% 219.91/171.00  																																									|-The branch is then unsatisfiable
% 219.91/171.00  																																								|-Branch two:
% 219.91/171.00  																																								| (1672) aNaturalNumber0(xk) = all_12_0_10
% 219.91/171.00  																																								| (1673) all_52_2_87 = all_12_0_10
% 219.91/171.00  																																								|
% 219.91/171.00  																																									| Combining equations (1281,1673) yields a new equation:
% 219.91/171.00  																																									| (1674) all_52_2_87 = 0
% 219.91/171.00  																																									|
% 219.91/171.00  																																									| From (1281) and (1672) follows:
% 219.91/171.00  																																									| (1665) aNaturalNumber0(xk) = 0
% 219.91/171.00  																																									|
% 219.91/171.00  																																									+-Applying beta-rule and splitting (214), into two cases.
% 219.91/171.00  																																									|-Branch one:
% 219.91/171.00  																																									| (1676)  ~ (all_52_0_85 = 0)
% 219.91/171.00  																																									|
% 219.91/171.00  																																										+-Applying beta-rule and splitting (1378), into two cases.
% 219.91/171.00  																																										|-Branch one:
% 219.91/171.00  																																										| (1677)  ~ (sdtasdt0(xp, all_28_2_36) = sz00)
% 220.31/171.00  																																										|
% 220.31/171.00  																																											| From (1663) and (1677) follows:
% 220.31/171.00  																																											| (1678)  ~ (sdtasdt0(xp, xk) = sz00)
% 220.31/171.00  																																											|
% 220.31/171.00  																																											+-Applying beta-rule and splitting (1517), into two cases.
% 220.31/171.00  																																											|-Branch one:
% 220.31/171.00  																																											| (1679) all_249_0_191 = xp & all_249_1_192 = 0 & sdtasdt0(all_99_0_112, all_249_2_193) = xp & aNaturalNumber0(all_249_2_193) = 0
% 220.31/171.00  																																											|
% 220.31/171.00  																																												| Applying alpha-rule on (1679) yields:
% 220.31/171.00  																																												| (1680) all_249_0_191 = xp
% 220.31/171.00  																																												| (1681) all_249_1_192 = 0
% 220.31/171.00  																																												| (1682) sdtasdt0(all_99_0_112, all_249_2_193) = xp
% 220.31/171.00  																																												| (1683) aNaturalNumber0(all_249_2_193) = 0
% 220.31/171.01  																																												|
% 220.31/171.01  																																												+-Applying beta-rule and splitting (1407), into two cases.
% 220.31/171.01  																																												|-Branch one:
% 220.31/171.01  																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.31/171.01  																																												|
% 220.31/171.01  																																													| Using (1665) and (1670) yields:
% 220.31/171.01  																																													| (1311) $false
% 220.31/171.01  																																													|
% 220.31/171.01  																																													|-The branch is then unsatisfiable
% 220.31/171.01  																																												|-Branch two:
% 220.31/171.01  																																												| (1665) aNaturalNumber0(xk) = 0
% 220.31/171.01  																																												| (1687) xk = sz10 | xk = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.01  																																												|
% 220.31/171.01  																																													+-Applying beta-rule and splitting (1405), into two cases.
% 220.31/171.01  																																													|-Branch one:
% 220.31/171.01  																																													| (1688) all_28_2_36 = sz00
% 220.31/171.01  																																													|
% 220.31/171.01  																																														| Combining equations (1663,1688) yields a new equation:
% 220.31/171.01  																																														| (1689) xk = sz00
% 220.31/171.01  																																														|
% 220.31/171.01  																																														| Simplifying 1689 yields:
% 220.31/171.01  																																														| (1690) xk = sz00
% 220.31/171.01  																																														|
% 220.31/171.01  																																														| Equations (1690) can reduce 27 to:
% 220.31/171.01  																																														| (197) $false
% 220.31/171.01  																																														|
% 220.31/171.01  																																														|-The branch is then unsatisfiable
% 220.31/171.01  																																													|-Branch two:
% 220.31/171.01  																																													| (1692)  ~ (all_28_2_36 = sz00)
% 220.31/171.01  																																													| (1693) all_28_2_36 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_28_2_36) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.01  																																													|
% 220.31/171.01  																																														| Equations (1663) can reduce 1692 to:
% 220.31/171.01  																																														| (27)  ~ (xk = sz00)
% 220.31/171.01  																																														|
% 220.31/171.01  																																														+-Applying beta-rule and splitting (1687), into two cases.
% 220.31/171.01  																																														|-Branch one:
% 220.31/171.01  																																														| (1690) xk = sz00
% 220.31/171.01  																																														|
% 220.31/171.01  																																															| Equations (1690) can reduce 27 to:
% 220.31/171.01  																																															| (197) $false
% 220.31/171.01  																																															|
% 220.31/171.01  																																															|-The branch is then unsatisfiable
% 220.31/171.01  																																														|-Branch two:
% 220.31/171.01  																																														| (27)  ~ (xk = sz00)
% 220.31/171.01  																																														| (1698) xk = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.01  																																														|
% 220.31/171.01  																																															+-Applying beta-rule and splitting (1394), into two cases.
% 220.31/171.01  																																															|-Branch one:
% 220.31/171.01  																																															| (1699) xp = xn
% 220.31/171.01  																																															|
% 220.31/171.01  																																																| Equations (1699) can reduce 87 to:
% 220.31/171.01  																																																| (197) $false
% 220.31/171.01  																																																|
% 220.31/171.01  																																																|-The branch is then unsatisfiable
% 220.31/171.01  																																															|-Branch two:
% 220.31/171.01  																																															| (87)  ~ (xp = xn)
% 220.31/171.01  																																															| (1702)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(xp, xm) = v3 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v4 = v3) &  ~ (all_37_1_62 = all_0_9_9))))
% 220.31/171.01  																																															|
% 220.31/171.01  																																																| Instantiating (1702) with all_395_0_204, all_395_1_205, all_395_2_206, all_395_3_207, all_395_4_208 yields:
% 220.31/171.01  																																																| (1703) sdtpldt0(xp, xm) = all_395_1_205 & sdtpldt0(xn, xm) = all_395_0_204 & aNaturalNumber0(xp) = all_395_3_207 & aNaturalNumber0(xm) = all_395_4_208 & aNaturalNumber0(xn) = all_395_2_206 & ( ~ (all_395_2_206 = 0) |  ~ (all_395_3_207 = 0) |  ~ (all_395_4_208 = 0) | ( ~ (all_395_0_204 = all_395_1_205) &  ~ (all_37_1_62 = all_0_9_9)))
% 220.31/171.01  																																																|
% 220.31/171.01  																																																| Applying alpha-rule on (1703) yields:
% 220.31/171.01  																																																| (1704) aNaturalNumber0(xp) = all_395_3_207
% 220.31/171.01  																																																| (1705) sdtpldt0(xp, xm) = all_395_1_205
% 220.31/171.01  																																																| (1706) aNaturalNumber0(xm) = all_395_4_208
% 220.31/171.01  																																																| (1707)  ~ (all_395_2_206 = 0) |  ~ (all_395_3_207 = 0) |  ~ (all_395_4_208 = 0) | ( ~ (all_395_0_204 = all_395_1_205) &  ~ (all_37_1_62 = all_0_9_9))
% 220.31/171.01  																																																| (1708) sdtpldt0(xn, xm) = all_395_0_204
% 220.31/171.01  																																																| (1709) aNaturalNumber0(xn) = all_395_2_206
% 220.31/171.01  																																																|
% 220.31/171.01  																																																+-Applying beta-rule and splitting (1509), into two cases.
% 220.31/171.01  																																																|-Branch one:
% 220.31/171.01  																																																| (1710)  ~ (all_244_2_182 = 0)
% 220.31/171.01  																																																|
% 220.31/171.01  																																																	| Equations (1647) can reduce 1710 to:
% 220.31/171.01  																																																	| (197) $false
% 220.31/171.01  																																																	|
% 220.31/171.01  																																																	|-The branch is then unsatisfiable
% 220.31/171.01  																																																|-Branch two:
% 220.31/171.01  																																																| (1647) all_244_2_182 = 0
% 220.31/171.01  																																																| (1713)  ~ (all_244_3_183 = 0) |  ~ (all_244_4_184 = 0) | all_244_0_180 = all_0_7_7
% 220.31/171.01  																																																|
% 220.31/171.01  																																																	+-Applying beta-rule and splitting (1366), into two cases.
% 220.31/171.01  																																																	|-Branch one:
% 220.31/171.01  																																																	| (1690) xk = sz00
% 220.31/171.01  																																																	|
% 220.31/171.01  																																																		| Equations (1690) can reduce 27 to:
% 220.31/171.01  																																																		| (197) $false
% 220.31/171.01  																																																		|
% 220.31/171.01  																																																		|-The branch is then unsatisfiable
% 220.31/171.01  																																																	|-Branch two:
% 220.31/171.01  																																																	| (27)  ~ (xk = sz00)
% 220.31/171.01  																																																	| (1717) all_52_0_85 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 220.31/171.01  																																																	|
% 220.31/171.01  																																																		+-Applying beta-rule and splitting (1713), into two cases.
% 220.31/171.01  																																																		|-Branch one:
% 220.31/171.01  																																																		| (1718)  ~ (all_244_3_183 = 0)
% 220.31/171.01  																																																		|
% 220.31/171.01  																																																			| Equations (1548) can reduce 1718 to:
% 220.31/171.01  																																																			| (197) $false
% 220.31/171.01  																																																			|
% 220.31/171.01  																																																			|-The branch is then unsatisfiable
% 220.31/171.01  																																																		|-Branch two:
% 220.31/171.01  																																																		| (1548) all_244_3_183 = 0
% 220.31/171.01  																																																		| (1721)  ~ (all_244_4_184 = 0) | all_244_0_180 = all_0_7_7
% 220.31/171.01  																																																		|
% 220.31/171.01  																																																			+-Applying beta-rule and splitting (1717), into two cases.
% 220.31/171.01  																																																			|-Branch one:
% 220.31/171.01  																																																			| (1722) all_52_0_85 = 0
% 220.31/171.01  																																																			|
% 220.31/171.01  																																																				| Equations (1722) can reduce 1676 to:
% 220.31/171.01  																																																				| (197) $false
% 220.31/171.01  																																																				|
% 220.31/171.01  																																																				|-The branch is then unsatisfiable
% 220.31/171.01  																																																			|-Branch two:
% 220.31/171.01  																																																			| (1676)  ~ (all_52_0_85 = 0)
% 220.31/171.01  																																																			| (1725)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 220.31/171.01  																																																			|
% 220.31/171.01  																																																				| Instantiating (1725) with all_475_0_209, all_475_1_210, all_475_2_211 yields:
% 220.31/171.01  																																																				| (1726) doDivides0(xp, xk) = all_475_0_209 & aNaturalNumber0(xk) = all_475_1_210 & aNaturalNumber0(xp) = all_475_2_211 & ( ~ (all_475_0_209 = 0) |  ~ (all_475_1_210 = 0) |  ~ (all_475_2_211 = 0))
% 220.31/171.01  																																																				|
% 220.31/171.01  																																																				| Applying alpha-rule on (1726) yields:
% 220.31/171.01  																																																				| (1727) doDivides0(xp, xk) = all_475_0_209
% 220.31/171.01  																																																				| (1728) aNaturalNumber0(xk) = all_475_1_210
% 220.31/171.01  																																																				| (1729) aNaturalNumber0(xp) = all_475_2_211
% 220.31/171.01  																																																				| (1730)  ~ (all_475_0_209 = 0) |  ~ (all_475_1_210 = 0) |  ~ (all_475_2_211 = 0)
% 220.31/171.01  																																																				|
% 220.31/171.01  																																																				+-Applying beta-rule and splitting (1721), into two cases.
% 220.31/171.01  																																																				|-Branch one:
% 220.31/171.01  																																																				| (1731)  ~ (all_244_4_184 = 0)
% 220.31/171.01  																																																				|
% 220.31/171.01  																																																					| Equations (1594) can reduce 1731 to:
% 220.31/171.01  																																																					| (197) $false
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					|-The branch is then unsatisfiable
% 220.31/171.01  																																																				|-Branch two:
% 220.31/171.01  																																																				| (1594) all_244_4_184 = 0
% 220.31/171.01  																																																				| (1734) all_244_0_180 = all_0_7_7
% 220.31/171.01  																																																				|
% 220.31/171.01  																																																					| From (1734) and (1510) follows:
% 220.31/171.01  																																																					| (1735) sdtasdt0(xr, all_244_1_181) = all_0_7_7
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Instantiating formula (28) with xk, all_475_1_210, 0 and discharging atoms aNaturalNumber0(xk) = all_475_1_210, aNaturalNumber0(xk) = 0, yields:
% 220.31/171.01  																																																					| (1736) all_475_1_210 = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Instantiating formula (28) with xp, all_475_2_211, 0 and discharging atoms aNaturalNumber0(xp) = all_475_2_211, aNaturalNumber0(xp) = 0, yields:
% 220.31/171.01  																																																					| (1737) all_475_2_211 = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Instantiating formula (28) with xp, all_395_3_207, all_475_2_211 and discharging atoms aNaturalNumber0(xp) = all_475_2_211, aNaturalNumber0(xp) = all_395_3_207, yields:
% 220.31/171.01  																																																					| (1738) all_475_2_211 = all_395_3_207
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Instantiating formula (28) with xm, all_395_4_208, 0 and discharging atoms aNaturalNumber0(xm) = all_395_4_208, aNaturalNumber0(xm) = 0, yields:
% 220.31/171.01  																																																					| (1739) all_395_4_208 = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Instantiating formula (28) with xn, all_395_2_206, 0 and discharging atoms aNaturalNumber0(xn) = all_395_2_206, aNaturalNumber0(xn) = 0, yields:
% 220.31/171.01  																																																					| (1740) all_395_2_206 = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Using (1664) and (1678) yields:
% 220.31/171.01  																																																					| (1741)  ~ (all_0_7_7 = sz00)
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Combining equations (1738,1737) yields a new equation:
% 220.31/171.01  																																																					| (1742) all_395_3_207 = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| Simplifying 1742 yields:
% 220.31/171.01  																																																					| (1743) all_395_3_207 = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| From (1736) and (1728) follows:
% 220.31/171.01  																																																					| (1665) aNaturalNumber0(xk) = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| From (1743) and (1704) follows:
% 220.31/171.01  																																																					| (9) aNaturalNumber0(xp) = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| From (1739) and (1706) follows:
% 220.31/171.01  																																																					| (12) aNaturalNumber0(xm) = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					| From (1740) and (1709) follows:
% 220.31/171.01  																																																					| (91) aNaturalNumber0(xn) = 0
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																					+-Applying beta-rule and splitting (1375), into two cases.
% 220.31/171.01  																																																					|-Branch one:
% 220.31/171.01  																																																					| (1748)  ~ (sdtasdt0(xp, all_28_2_36) = xn)
% 220.31/171.01  																																																					|
% 220.31/171.01  																																																						| From (1663) and (1748) follows:
% 220.31/171.01  																																																						| (1749)  ~ (sdtasdt0(xp, xk) = xn)
% 220.31/171.01  																																																						|
% 220.31/171.01  																																																						+-Applying beta-rule and splitting (1395), into two cases.
% 220.31/171.01  																																																						|-Branch one:
% 220.31/171.01  																																																						| (1699) xp = xn
% 220.31/171.01  																																																						|
% 220.31/171.01  																																																							| Equations (1699) can reduce 87 to:
% 220.31/171.01  																																																							| (197) $false
% 220.31/171.01  																																																							|
% 220.31/171.01  																																																							|-The branch is then unsatisfiable
% 220.31/171.01  																																																						|-Branch two:
% 220.31/171.01  																																																						| (87)  ~ (xp = xn)
% 220.31/171.01  																																																						| (1753)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtpldt0(xp, xm) = v4 & sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v4 = v3) &  ~ (all_37_1_62 = all_0_9_9))))
% 220.31/171.01  																																																						|
% 220.31/171.01  																																																							| Instantiating (1753) with all_505_0_212, all_505_1_213, all_505_2_214, all_505_3_215, all_505_4_216 yields:
% 220.31/171.01  																																																							| (1754) sdtpldt0(xp, xm) = all_505_0_212 & sdtpldt0(xn, xm) = all_505_1_213 & aNaturalNumber0(xp) = all_505_2_214 & aNaturalNumber0(xm) = all_505_4_216 & aNaturalNumber0(xn) = all_505_3_215 & ( ~ (all_505_2_214 = 0) |  ~ (all_505_3_215 = 0) |  ~ (all_505_4_216 = 0) | ( ~ (all_505_0_212 = all_505_1_213) &  ~ (all_37_1_62 = all_0_9_9)))
% 220.31/171.01  																																																							|
% 220.31/171.01  																																																							| Applying alpha-rule on (1754) yields:
% 220.31/171.01  																																																							| (1755)  ~ (all_505_2_214 = 0) |  ~ (all_505_3_215 = 0) |  ~ (all_505_4_216 = 0) | ( ~ (all_505_0_212 = all_505_1_213) &  ~ (all_37_1_62 = all_0_9_9))
% 220.31/171.01  																																																							| (1756) aNaturalNumber0(xn) = all_505_3_215
% 220.31/171.02  																																																							| (1757) aNaturalNumber0(xm) = all_505_4_216
% 220.31/171.02  																																																							| (1758) aNaturalNumber0(xp) = all_505_2_214
% 220.31/171.02  																																																							| (1759) sdtpldt0(xn, xm) = all_505_1_213
% 220.31/171.02  																																																							| (1760) sdtpldt0(xp, xm) = all_505_0_212
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| Instantiating formula (28) with xp, all_505_2_214, 0 and discharging atoms aNaturalNumber0(xp) = all_505_2_214, aNaturalNumber0(xp) = 0, yields:
% 220.31/171.02  																																																							| (1761) all_505_2_214 = 0
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| Instantiating formula (28) with xm, all_505_4_216, 0 and discharging atoms aNaturalNumber0(xm) = all_505_4_216, aNaturalNumber0(xm) = 0, yields:
% 220.31/171.02  																																																							| (1762) all_505_4_216 = 0
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| Instantiating formula (28) with xn, all_505_3_215, 0 and discharging atoms aNaturalNumber0(xn) = all_505_3_215, aNaturalNumber0(xn) = 0, yields:
% 220.31/171.02  																																																							| (1763) all_505_3_215 = 0
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| Using (1664) and (1749) yields:
% 220.31/171.02  																																																							| (1764)  ~ (all_0_7_7 = xn)
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| From (1761) and (1758) follows:
% 220.31/171.02  																																																							| (9) aNaturalNumber0(xp) = 0
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| From (1762) and (1757) follows:
% 220.31/171.02  																																																							| (12) aNaturalNumber0(xm) = 0
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							| From (1763) and (1756) follows:
% 220.31/171.02  																																																							| (91) aNaturalNumber0(xn) = 0
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																							+-Applying beta-rule and splitting (1386), into two cases.
% 220.31/171.02  																																																							|-Branch one:
% 220.31/171.02  																																																							| (1768)  ~ (sdtasdt0(sz00, xn) = all_0_7_7)
% 220.31/171.02  																																																							|
% 220.31/171.02  																																																								+-Applying beta-rule and splitting (1372), into two cases.
% 220.31/171.02  																																																								|-Branch one:
% 220.31/171.02  																																																								| (274) xr = sz00
% 220.31/171.02  																																																								|
% 220.31/171.02  																																																									| Equations (274) can reduce 100 to:
% 220.31/171.02  																																																									| (197) $false
% 220.31/171.02  																																																									|
% 220.31/171.02  																																																									|-The branch is then unsatisfiable
% 220.31/171.02  																																																								|-Branch two:
% 220.31/171.02  																																																								| (100)  ~ (xr = sz00)
% 220.31/171.02  																																																								| (1772) all_34_2_54 = all_0_3_3 |  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_34_2_54) = v0) | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))))
% 220.31/171.02  																																																								|
% 220.31/171.02  																																																									+-Applying beta-rule and splitting (1772), into two cases.
% 220.31/171.02  																																																									|-Branch one:
% 220.31/171.02  																																																									| (1773) all_34_2_54 = all_0_3_3
% 220.31/171.02  																																																									|
% 220.31/171.02  																																																										| From (1773) and (1506) follows:
% 220.31/171.02  																																																										| (1774) sdtasdt0(all_0_3_3, xm) = all_244_1_181
% 220.31/171.02  																																																										|
% 220.31/171.02  																																																										| From (1773) and (1342) follows:
% 220.31/171.02  																																																										| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.02  																																																										|
% 220.31/171.02  																																																										+-Applying beta-rule and splitting (1362), into two cases.
% 220.31/171.02  																																																										|-Branch one:
% 220.31/171.02  																																																										| (1776) all_99_0_112 = xp
% 220.31/171.02  																																																										|
% 220.31/171.02  																																																											| From (1776) and (1682) follows:
% 220.31/171.02  																																																											| (1777) sdtasdt0(xp, all_249_2_193) = xp
% 220.31/171.02  																																																											|
% 220.31/171.02  																																																											| From (1776) and (297) follows:
% 220.31/171.02  																																																											| (9) aNaturalNumber0(xp) = 0
% 220.31/171.02  																																																											|
% 220.31/171.02  																																																											+-Applying beta-rule and splitting (1556), into two cases.
% 220.31/171.02  																																																											|-Branch one:
% 220.31/171.02  																																																											| (1779)  ~ (aNaturalNumber0(all_0_3_3) = all_216_2_118)
% 220.31/171.02  																																																											|
% 220.31/171.02  																																																												| From (1637) and (1779) follows:
% 220.31/171.02  																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Using (1775) and (1780) yields:
% 220.31/171.02  																																																												| (1311) $false
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												|-The branch is then unsatisfiable
% 220.31/171.02  																																																											|-Branch two:
% 220.31/171.02  																																																											| (1782) aNaturalNumber0(all_0_3_3) = all_216_2_118
% 220.31/171.02  																																																											| (1783) all_250_1_195 = all_216_2_118
% 220.31/171.02  																																																											|
% 220.31/171.02  																																																												| Combining equations (1783,1555) yields a new equation:
% 220.31/171.02  																																																												| (1784) all_216_2_118 = all_20_2_24
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Simplifying 1784 yields:
% 220.31/171.02  																																																												| (1785) all_216_2_118 = all_20_2_24
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Combining equations (1785,1637) yields a new equation:
% 220.31/171.02  																																																												| (1786) all_20_2_24 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Simplifying 1786 yields:
% 220.31/171.02  																																																												| (1787) all_20_2_24 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Combining equations (1787,1183) yields a new equation:
% 220.31/171.02  																																																												| (1788) all_22_2_27 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Combining equations (1787,1178) yields a new equation:
% 220.31/171.02  																																																												| (1789) all_57_2_90 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Combining equations (1787,1168) yields a new equation:
% 220.31/171.02  																																																												| (1790) all_62_2_94 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| Combining equations (1787,378) yields a new equation:
% 220.31/171.02  																																																												| (1791) all_72_2_101 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												| From (1787) and (154) follows:
% 220.31/171.02  																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																												+-Applying beta-rule and splitting (156), into two cases.
% 220.31/171.02  																																																												|-Branch one:
% 220.31/171.02  																																																												| (1793)  ~ (all_20_1_23 = 0)
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																													| Equations (1228) can reduce 1793 to:
% 220.31/171.02  																																																													| (197) $false
% 220.31/171.02  																																																													|
% 220.31/171.02  																																																													|-The branch is then unsatisfiable
% 220.31/171.02  																																																												|-Branch two:
% 220.31/171.02  																																																												| (1228) all_20_1_23 = 0
% 220.31/171.02  																																																												| (1796)  ~ (all_20_2_24 = 0) | all_20_0_22 = 0
% 220.31/171.02  																																																												|
% 220.31/171.02  																																																													+-Applying beta-rule and splitting (1368), into two cases.
% 220.31/171.02  																																																													|-Branch one:
% 220.31/171.02  																																																													| (1797)  ~ (sdtlseqdt0(xn, all_0_3_3) = 0)
% 220.31/171.02  																																																													|
% 220.31/171.02  																																																														+-Applying beta-rule and splitting (161), into two cases.
% 220.31/171.02  																																																														|-Branch one:
% 220.31/171.02  																																																														| (1798)  ~ (all_22_1_26 = 0)
% 220.31/171.02  																																																														|
% 220.31/171.02  																																																															| Equations (1229) can reduce 1798 to:
% 220.31/171.02  																																																															| (197) $false
% 220.31/171.02  																																																															|
% 220.31/171.02  																																																															|-The branch is then unsatisfiable
% 220.31/171.02  																																																														|-Branch two:
% 220.31/171.02  																																																														| (1229) all_22_1_26 = 0
% 220.31/171.02  																																																														| (1801)  ~ (all_22_2_27 = 0) | all_22_0_25 = all_0_2_2
% 220.31/171.02  																																																														|
% 220.31/171.02  																																																															+-Applying beta-rule and splitting (233), into two cases.
% 220.31/171.02  																																																															|-Branch one:
% 220.31/171.02  																																																															| (1802)  ~ (all_62_0_92 = 0)
% 220.31/171.02  																																																															|
% 220.31/171.02  																																																																+-Applying beta-rule and splitting (1801), into two cases.
% 220.31/171.02  																																																																|-Branch one:
% 220.31/171.02  																																																																| (1803)  ~ (all_22_2_27 = 0)
% 220.31/171.02  																																																																|
% 220.31/171.02  																																																																	| Equations (1788) can reduce 1803 to:
% 220.31/171.02  																																																																	| (197) $false
% 220.31/171.02  																																																																	|
% 220.31/171.02  																																																																	|-The branch is then unsatisfiable
% 220.31/171.02  																																																																|-Branch two:
% 220.31/171.02  																																																																| (1788) all_22_2_27 = 0
% 220.31/171.02  																																																																| (1806) all_22_0_25 = all_0_2_2
% 220.31/171.02  																																																																|
% 220.31/171.02  																																																																	| From (1806) and (158) follows:
% 220.31/171.02  																																																																	| (1807) sdtasdt0(xm, all_0_3_3) = all_0_2_2
% 220.31/171.02  																																																																	|
% 220.31/171.02  																																																																	| From (1806) and (1478) follows:
% 220.31/171.02  																																																																	| (1808) aNaturalNumber0(all_0_2_2) = all_236_0_160
% 220.31/171.02  																																																																	|
% 220.31/171.02  																																																																	+-Applying beta-rule and splitting (174), into two cases.
% 220.31/171.02  																																																																	|-Branch one:
% 220.31/171.02  																																																																	| (1809) all_32_0_46 = xn & all_32_1_47 = 0 & sdtpldt0(all_0_3_3, all_32_2_48) = xn & aNaturalNumber0(all_32_2_48) = 0
% 220.31/171.02  																																																																	|
% 220.31/171.02  																																																																		| Applying alpha-rule on (1809) yields:
% 220.31/171.02  																																																																		| (1810) all_32_0_46 = xn
% 220.31/171.02  																																																																		| (1811) all_32_1_47 = 0
% 220.31/171.02  																																																																		| (1812) sdtpldt0(all_0_3_3, all_32_2_48) = xn
% 220.31/171.02  																																																																		| (1813) aNaturalNumber0(all_32_2_48) = 0
% 220.31/171.02  																																																																		|
% 220.31/171.02  																																																																		+-Applying beta-rule and splitting (1544), into two cases.
% 220.31/171.02  																																																																		|-Branch one:
% 220.31/171.02  																																																																		| (1814)  ~ (sdtasdt0(all_0_3_3, xm) = all_244_1_181)
% 220.31/171.02  																																																																		|
% 220.31/171.02  																																																																			| Using (1774) and (1814) yields:
% 220.31/171.02  																																																																			| (1311) $false
% 220.31/171.02  																																																																			|
% 220.31/171.02  																																																																			|-The branch is then unsatisfiable
% 220.31/171.02  																																																																		|-Branch two:
% 220.31/171.02  																																																																		| (1774) sdtasdt0(all_0_3_3, xm) = all_244_1_181
% 220.31/171.02  																																																																		| (1817) all_244_1_181 = all_0_2_2
% 220.31/171.02  																																																																		|
% 220.31/171.02  																																																																			| From (1817) and (1774) follows:
% 220.31/171.02  																																																																			| (45) sdtasdt0(all_0_3_3, xm) = all_0_2_2
% 220.31/171.02  																																																																			|
% 220.31/171.02  																																																																			| From (1817) and (1735) follows:
% 220.31/171.02  																																																																			| (1819) sdtasdt0(xr, all_0_2_2) = all_0_7_7
% 220.31/171.02  																																																																			|
% 220.31/171.02  																																																																			+-Applying beta-rule and splitting (1554), into two cases.
% 220.31/171.02  																																																																			|-Branch one:
% 220.31/171.02  																																																																			| (1820)  ~ (aNaturalNumber0(all_0_2_2) = all_236_0_160)
% 220.31/171.02  																																																																			|
% 220.31/171.02  																																																																				| Using (1808) and (1820) yields:
% 220.31/171.02  																																																																				| (1311) $false
% 220.31/171.02  																																																																				|
% 220.31/171.02  																																																																				|-The branch is then unsatisfiable
% 220.31/171.02  																																																																			|-Branch two:
% 220.31/171.02  																																																																			| (1808) aNaturalNumber0(all_0_2_2) = all_236_0_160
% 220.31/171.02  																																																																			| (1823) all_236_0_160 = all_20_0_22
% 220.31/171.02  																																																																			|
% 220.31/171.02  																																																																				| From (1823) and (1808) follows:
% 220.31/171.02  																																																																				| (153) aNaturalNumber0(all_0_2_2) = all_20_0_22
% 220.31/171.02  																																																																				|
% 220.31/171.02  																																																																				+-Applying beta-rule and splitting (1796), into two cases.
% 220.31/171.02  																																																																				|-Branch one:
% 220.31/171.02  																																																																				| (1825)  ~ (all_20_2_24 = 0)
% 220.31/171.02  																																																																				|
% 220.31/171.02  																																																																					| Equations (1787) can reduce 1825 to:
% 220.31/171.02  																																																																					| (197) $false
% 220.31/171.02  																																																																					|
% 220.31/171.02  																																																																					|-The branch is then unsatisfiable
% 220.31/171.02  																																																																				|-Branch two:
% 220.31/171.02  																																																																				| (1787) all_20_2_24 = 0
% 220.31/171.02  																																																																				| (1828) all_20_0_22 = 0
% 220.31/171.02  																																																																				|
% 220.31/171.02  																																																																					| Combining equations (1828,1156) yields a new equation:
% 220.31/171.02  																																																																					| (1829) all_67_2_97 = 0
% 220.31/171.02  																																																																					|
% 220.31/171.02  																																																																					| Combining equations (1828,330) yields a new equation:
% 220.31/171.02  																																																																					| (1830) all_82_2_109 = 0
% 220.31/171.02  																																																																					|
% 220.31/171.02  																																																																					| From (1828) and (153) follows:
% 220.31/171.02  																																																																					| (1831) aNaturalNumber0(all_0_2_2) = 0
% 220.31/171.02  																																																																					|
% 220.31/171.02  																																																																					+-Applying beta-rule and splitting (1367), into two cases.
% 220.31/171.02  																																																																					|-Branch one:
% 220.31/171.02  																																																																					| (1832) all_62_0_92 = 0
% 220.31/171.02  																																																																					|
% 220.31/171.02  																																																																						| Equations (1832) can reduce 1802 to:
% 220.31/171.02  																																																																						| (197) $false
% 220.31/171.02  																																																																						|
% 220.31/171.02  																																																																						|-The branch is then unsatisfiable
% 220.31/171.02  																																																																					|-Branch two:
% 220.31/171.02  																																																																					| (1802)  ~ (all_62_0_92 = 0)
% 220.31/171.02  																																																																					| (1835)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtlseqdt0(xp, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 220.31/171.02  																																																																					|
% 220.31/171.03  																																																																						| Instantiating (1835) with all_642_0_217, all_642_1_218, all_642_2_219, all_642_3_220 yields:
% 220.31/171.03  																																																																						| (1836) sdtlseqdt0(xp, all_0_3_3) = all_642_0_217 & aNaturalNumber0(all_0_3_3) = all_642_1_218 & aNaturalNumber0(xp) = all_642_2_219 & aNaturalNumber0(xn) = all_642_3_220 & ( ~ (all_642_0_217 = 0) |  ~ (all_642_1_218 = 0) |  ~ (all_642_2_219 = 0) |  ~ (all_642_3_220 = 0))
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| Applying alpha-rule on (1836) yields:
% 220.31/171.03  																																																																						| (1837) aNaturalNumber0(xp) = all_642_2_219
% 220.31/171.03  																																																																						| (1838) aNaturalNumber0(xn) = all_642_3_220
% 220.31/171.03  																																																																						| (1839) sdtlseqdt0(xp, all_0_3_3) = all_642_0_217
% 220.31/171.03  																																																																						| (1840) aNaturalNumber0(all_0_3_3) = all_642_1_218
% 220.31/171.03  																																																																						| (1841)  ~ (all_642_0_217 = 0) |  ~ (all_642_1_218 = 0) |  ~ (all_642_2_219 = 0) |  ~ (all_642_3_220 = 0)
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| Instantiating formula (28) with all_0_3_3, all_642_1_218, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_642_1_218, aNaturalNumber0(all_0_3_3) = 0, yields:
% 220.31/171.03  																																																																						| (1842) all_642_1_218 = 0
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| Instantiating formula (28) with xp, all_642_2_219, 0 and discharging atoms aNaturalNumber0(xp) = all_642_2_219, aNaturalNumber0(xp) = 0, yields:
% 220.31/171.03  																																																																						| (1843) all_642_2_219 = 0
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| Instantiating formula (28) with xn, all_642_3_220, 0 and discharging atoms aNaturalNumber0(xn) = all_642_3_220, aNaturalNumber0(xn) = 0, yields:
% 220.31/171.03  																																																																						| (1844) all_642_3_220 = 0
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| Using (1277) and (1768) yields:
% 220.31/171.03  																																																																						| (1845)  ~ (xm = sz00)
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| From (1842) and (1840) follows:
% 220.31/171.03  																																																																						| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| From (1843) and (1837) follows:
% 220.31/171.03  																																																																						| (9) aNaturalNumber0(xp) = 0
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						| From (1844) and (1838) follows:
% 220.31/171.03  																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																						+-Applying beta-rule and splitting (1841), into two cases.
% 220.31/171.03  																																																																						|-Branch one:
% 220.31/171.03  																																																																						| (1849)  ~ (all_642_0_217 = 0)
% 220.31/171.03  																																																																						|
% 220.31/171.03  																																																																							+-Applying beta-rule and splitting (1384), into two cases.
% 220.31/171.03  																																																																							|-Branch one:
% 220.31/171.03  																																																																							| (1850) xm = sz00
% 220.31/171.03  																																																																							|
% 220.31/171.03  																																																																								| Equations (1850) can reduce 1845 to:
% 220.31/171.03  																																																																								| (197) $false
% 220.31/171.03  																																																																								|
% 220.31/171.03  																																																																								|-The branch is then unsatisfiable
% 220.31/171.03  																																																																							|-Branch two:
% 220.31/171.03  																																																																							| (1845)  ~ (xm = sz00)
% 220.31/171.03  																																																																							| (1853) all_0_3_3 = xn |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(all_0_3_3, xm) = v2 & sdtasdt0(xn, xm) = v3 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v3 = v2) &  ~ (all_22_0_25 = all_0_7_7))))
% 220.31/171.03  																																																																							|
% 220.31/171.03  																																																																								+-Applying beta-rule and splitting (1365), into two cases.
% 220.31/171.03  																																																																								|-Branch one:
% 220.31/171.03  																																																																								| (1854)  ~ (sdtasdt0(all_0_3_3, xm) = xm)
% 220.31/171.03  																																																																								|
% 220.31/171.03  																																																																									+-Applying beta-rule and splitting (131), into two cases.
% 220.31/171.03  																																																																									|-Branch one:
% 220.31/171.03  																																																																									| (1850) xm = sz00
% 220.31/171.03  																																																																									|
% 220.31/171.03  																																																																										| Equations (1850) can reduce 1845 to:
% 220.31/171.03  																																																																										| (197) $false
% 220.31/171.03  																																																																										|
% 220.31/171.03  																																																																										|-The branch is then unsatisfiable
% 220.31/171.03  																																																																									|-Branch two:
% 220.31/171.03  																																																																									| (1845)  ~ (xm = sz00)
% 220.31/171.03  																																																																									| (1858) xm = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xm) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.03  																																																																									|
% 220.31/171.03  																																																																										+-Applying beta-rule and splitting (1385), into two cases.
% 220.31/171.03  																																																																										|-Branch one:
% 220.31/171.03  																																																																										| (1850) xm = sz00
% 220.31/171.03  																																																																										|
% 220.31/171.03  																																																																											| Equations (1850) can reduce 1845 to:
% 220.31/171.03  																																																																											| (197) $false
% 220.31/171.03  																																																																											|
% 220.31/171.03  																																																																											|-The branch is then unsatisfiable
% 220.31/171.03  																																																																										|-Branch two:
% 220.31/171.03  																																																																										| (1845)  ~ (xm = sz00)
% 220.31/171.03  																																																																										| (1862) all_0_3_3 = xn |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(all_0_3_3, xm) = v3 & sdtasdt0(xn, xm) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v3 = v2) &  ~ (all_22_0_25 = all_0_7_7))))
% 220.31/171.03  																																																																										|
% 220.31/171.03  																																																																											+-Applying beta-rule and splitting (1853), into two cases.
% 220.31/171.03  																																																																											|-Branch one:
% 220.31/171.03  																																																																											| (225) all_0_3_3 = xn
% 220.31/171.03  																																																																											|
% 220.31/171.03  																																																																												| Equations (225) can reduce 35 to:
% 220.31/171.03  																																																																												| (197) $false
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												|-The branch is then unsatisfiable
% 220.31/171.03  																																																																											|-Branch two:
% 220.31/171.03  																																																																											| (35)  ~ (all_0_3_3 = xn)
% 220.31/171.03  																																																																											| (1866)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(all_0_3_3, xm) = v2 & sdtasdt0(xn, xm) = v3 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v3 = v2) &  ~ (all_22_0_25 = all_0_7_7))))
% 220.31/171.03  																																																																											|
% 220.31/171.03  																																																																												| Instantiating (1866) with all_727_0_222, all_727_1_223, all_727_2_224, all_727_3_225 yields:
% 220.31/171.03  																																																																												| (1867) sdtasdt0(all_0_3_3, xm) = all_727_1_223 & sdtasdt0(xn, xm) = all_727_0_222 & aNaturalNumber0(all_0_3_3) = all_727_3_225 & aNaturalNumber0(xn) = all_727_2_224 & ( ~ (all_727_2_224 = 0) |  ~ (all_727_3_225 = 0) | ( ~ (all_727_0_222 = all_727_1_223) &  ~ (all_22_0_25 = all_0_7_7)))
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| Applying alpha-rule on (1867) yields:
% 220.31/171.03  																																																																												| (1868) aNaturalNumber0(all_0_3_3) = all_727_3_225
% 220.31/171.03  																																																																												| (1869) sdtasdt0(xn, xm) = all_727_0_222
% 220.31/171.03  																																																																												| (1870) sdtasdt0(all_0_3_3, xm) = all_727_1_223
% 220.31/171.03  																																																																												| (1871) aNaturalNumber0(xn) = all_727_2_224
% 220.31/171.03  																																																																												| (1872)  ~ (all_727_2_224 = 0) |  ~ (all_727_3_225 = 0) | ( ~ (all_727_0_222 = all_727_1_223) &  ~ (all_22_0_25 = all_0_7_7))
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| Instantiating formula (49) with all_0_3_3, xm, all_727_1_223, all_0_2_2 and discharging atoms sdtasdt0(all_0_3_3, xm) = all_727_1_223, sdtasdt0(all_0_3_3, xm) = all_0_2_2, yields:
% 220.31/171.03  																																																																												| (1873) all_727_1_223 = all_0_2_2
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| Instantiating formula (28) with all_0_3_3, all_727_3_225, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_727_3_225, aNaturalNumber0(all_0_3_3) = 0, yields:
% 220.31/171.03  																																																																												| (1874) all_727_3_225 = 0
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| Instantiating formula (28) with xn, all_727_2_224, 0 and discharging atoms aNaturalNumber0(xn) = all_727_2_224, aNaturalNumber0(xn) = 0, yields:
% 220.31/171.03  																																																																												| (1875) all_727_2_224 = 0
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| From (1873) and (1870) follows:
% 220.31/171.03  																																																																												| (45) sdtasdt0(all_0_3_3, xm) = all_0_2_2
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| From (1874) and (1868) follows:
% 220.31/171.03  																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												| From (1875) and (1871) follows:
% 220.31/171.03  																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																												+-Applying beta-rule and splitting (1862), into two cases.
% 220.31/171.03  																																																																												|-Branch one:
% 220.31/171.03  																																																																												| (225) all_0_3_3 = xn
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																													| Equations (225) can reduce 35 to:
% 220.31/171.03  																																																																													| (197) $false
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													|-The branch is then unsatisfiable
% 220.31/171.03  																																																																												|-Branch two:
% 220.31/171.03  																																																																												| (35)  ~ (all_0_3_3 = xn)
% 220.31/171.03  																																																																												| (1882)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(all_0_3_3, xm) = v3 & sdtasdt0(xn, xm) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | ( ~ (v3 = v2) &  ~ (all_22_0_25 = all_0_7_7))))
% 220.31/171.03  																																																																												|
% 220.31/171.03  																																																																													| Instantiating (1882) with all_747_0_227, all_747_1_228, all_747_2_229, all_747_3_230 yields:
% 220.31/171.03  																																																																													| (1883) sdtasdt0(all_0_3_3, xm) = all_747_0_227 & sdtasdt0(xn, xm) = all_747_1_228 & aNaturalNumber0(all_0_3_3) = all_747_2_229 & aNaturalNumber0(xn) = all_747_3_230 & ( ~ (all_747_2_229 = 0) |  ~ (all_747_3_230 = 0) | ( ~ (all_747_0_227 = all_747_1_228) &  ~ (all_22_0_25 = all_0_7_7)))
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| Applying alpha-rule on (1883) yields:
% 220.31/171.03  																																																																													| (1884) sdtasdt0(xn, xm) = all_747_1_228
% 220.31/171.03  																																																																													| (1885) sdtasdt0(all_0_3_3, xm) = all_747_0_227
% 220.31/171.03  																																																																													| (1886) aNaturalNumber0(xn) = all_747_3_230
% 220.31/171.03  																																																																													| (1887)  ~ (all_747_2_229 = 0) |  ~ (all_747_3_230 = 0) | ( ~ (all_747_0_227 = all_747_1_228) &  ~ (all_22_0_25 = all_0_7_7))
% 220.31/171.03  																																																																													| (1888) aNaturalNumber0(all_0_3_3) = all_747_2_229
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| Instantiating formula (49) with all_0_3_3, xm, all_747_0_227, all_0_2_2 and discharging atoms sdtasdt0(all_0_3_3, xm) = all_747_0_227, sdtasdt0(all_0_3_3, xm) = all_0_2_2, yields:
% 220.31/171.03  																																																																													| (1889) all_747_0_227 = all_0_2_2
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| Using (1885) and (1854) yields:
% 220.31/171.03  																																																																													| (1890)  ~ (all_747_0_227 = xm)
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| Instantiating formula (28) with all_0_3_3, all_747_2_229, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_747_2_229, aNaturalNumber0(all_0_3_3) = 0, yields:
% 220.31/171.03  																																																																													| (1891) all_747_2_229 = 0
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| Instantiating formula (28) with xn, all_747_3_230, 0 and discharging atoms aNaturalNumber0(xn) = all_747_3_230, aNaturalNumber0(xn) = 0, yields:
% 220.31/171.03  																																																																													| (1892) all_747_3_230 = 0
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| Equations (1889) can reduce 1890 to:
% 220.31/171.03  																																																																													| (1893)  ~ (all_0_2_2 = xm)
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| From (1889) and (1885) follows:
% 220.31/171.03  																																																																													| (45) sdtasdt0(all_0_3_3, xm) = all_0_2_2
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| From (1891) and (1888) follows:
% 220.31/171.03  																																																																													| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													| From (1892) and (1886) follows:
% 220.31/171.03  																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																													+-Applying beta-rule and splitting (118), into two cases.
% 220.31/171.03  																																																																													|-Branch one:
% 220.31/171.03  																																																																													| (1897)  ~ (sdtasdt0(sz00, xm) = all_0_2_2)
% 220.31/171.03  																																																																													|
% 220.31/171.03  																																																																														| Using (45) and (1897) yields:
% 220.31/171.03  																																																																														| (1898)  ~ (all_0_3_3 = sz00)
% 220.31/171.03  																																																																														|
% 220.31/171.03  																																																																														+-Applying beta-rule and splitting (1404), into two cases.
% 220.31/171.03  																																																																														|-Branch one:
% 220.31/171.03  																																																																														| (1899) all_34_2_54 = sz00
% 220.31/171.03  																																																																														|
% 220.31/171.03  																																																																															| Combining equations (1773,1899) yields a new equation:
% 220.31/171.03  																																																																															| (1900) all_0_3_3 = sz00
% 220.31/171.03  																																																																															|
% 220.31/171.03  																																																																															| Simplifying 1900 yields:
% 220.31/171.03  																																																																															| (1901) all_0_3_3 = sz00
% 220.31/171.03  																																																																															|
% 220.31/171.03  																																																																															| Equations (1901) can reduce 1898 to:
% 220.31/171.03  																																																																															| (197) $false
% 220.31/171.03  																																																																															|
% 220.31/171.03  																																																																															|-The branch is then unsatisfiable
% 220.31/171.03  																																																																														|-Branch two:
% 220.31/171.03  																																																																														| (1903)  ~ (all_34_2_54 = sz00)
% 220.31/171.03  																																																																														| (1904) all_34_2_54 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_34_2_54) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.03  																																																																														|
% 220.31/171.04  																																																																															| Equations (1773) can reduce 1903 to:
% 220.31/171.04  																																																																															| (1898)  ~ (all_0_3_3 = sz00)
% 220.31/171.04  																																																																															|
% 220.31/171.04  																																																																															+-Applying beta-rule and splitting (1370), into two cases.
% 220.31/171.04  																																																																															|-Branch one:
% 220.31/171.04  																																																																															| (1901) all_0_3_3 = sz00
% 220.31/171.04  																																																																															|
% 220.31/171.04  																																																																																| Equations (1901) can reduce 1898 to:
% 220.31/171.04  																																																																																| (197) $false
% 220.31/171.04  																																																																																|
% 220.31/171.04  																																																																																|-The branch is then unsatisfiable
% 220.31/171.04  																																																																															|-Branch two:
% 220.31/171.04  																																																																															| (1898)  ~ (all_0_3_3 = sz00)
% 220.31/171.04  																																																																															| (1909) all_62_0_92 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 220.31/171.04  																																																																															|
% 220.31/171.04  																																																																																+-Applying beta-rule and splitting (1406), into two cases.
% 220.31/171.04  																																																																																|-Branch one:
% 220.31/171.04  																																																																																| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 220.31/171.04  																																																																																|
% 220.31/171.04  																																																																																	| Using (1775) and (1780) yields:
% 220.31/171.04  																																																																																	| (1311) $false
% 220.31/171.04  																																																																																	|
% 220.31/171.04  																																																																																	|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																|-Branch two:
% 220.31/171.04  																																																																																| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.04  																																																																																| (1913) all_0_3_3 = sz10 | all_0_3_3 = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_0_3_3) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.04  																																																																																|
% 220.31/171.04  																																																																																	+-Applying beta-rule and splitting (1909), into two cases.
% 220.31/171.04  																																																																																	|-Branch one:
% 220.31/171.04  																																																																																	| (1832) all_62_0_92 = 0
% 220.31/171.04  																																																																																	|
% 220.31/171.04  																																																																																		| Equations (1832) can reduce 1802 to:
% 220.31/171.04  																																																																																		| (197) $false
% 220.31/171.04  																																																																																		|
% 220.31/171.04  																																																																																		|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																	|-Branch two:
% 220.31/171.04  																																																																																	| (1802)  ~ (all_62_0_92 = 0)
% 220.31/171.04  																																																																																	| (1917)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 220.31/171.04  																																																																																	|
% 220.31/171.04  																																																																																		| Instantiating (1917) with all_903_0_442, all_903_1_443, all_903_2_444 yields:
% 220.31/171.04  																																																																																		| (1918) doDivides0(xn, all_0_3_3) = all_903_0_442 & aNaturalNumber0(all_0_3_3) = all_903_1_443 & aNaturalNumber0(xn) = all_903_2_444 & ( ~ (all_903_0_442 = 0) |  ~ (all_903_1_443 = 0) |  ~ (all_903_2_444 = 0))
% 220.31/171.04  																																																																																		|
% 220.31/171.04  																																																																																		| Applying alpha-rule on (1918) yields:
% 220.31/171.04  																																																																																		| (1919) doDivides0(xn, all_0_3_3) = all_903_0_442
% 220.31/171.04  																																																																																		| (1920) aNaturalNumber0(all_0_3_3) = all_903_1_443
% 220.31/171.04  																																																																																		| (1921) aNaturalNumber0(xn) = all_903_2_444
% 220.31/171.04  																																																																																		| (1922)  ~ (all_903_0_442 = 0) |  ~ (all_903_1_443 = 0) |  ~ (all_903_2_444 = 0)
% 220.31/171.04  																																																																																		|
% 220.31/171.04  																																																																																		+-Applying beta-rule and splitting (1913), into two cases.
% 220.31/171.04  																																																																																		|-Branch one:
% 220.31/171.04  																																																																																		| (1901) all_0_3_3 = sz00
% 220.31/171.04  																																																																																		|
% 220.31/171.04  																																																																																			| Equations (1901) can reduce 1898 to:
% 220.31/171.04  																																																																																			| (197) $false
% 220.31/171.04  																																																																																			|
% 220.31/171.04  																																																																																			|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																		|-Branch two:
% 220.31/171.04  																																																																																		| (1898)  ~ (all_0_3_3 = sz00)
% 220.31/171.04  																																																																																		| (1926) all_0_3_3 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_0_3_3) = 0 & aNaturalNumber0(v0) = 0)
% 220.31/171.04  																																																																																		|
% 220.31/171.04  																																																																																			| Instantiating formula (28) with all_0_3_3, all_903_1_443, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_903_1_443, aNaturalNumber0(all_0_3_3) = 0, yields:
% 220.31/171.04  																																																																																			| (1927) all_903_1_443 = 0
% 220.31/171.04  																																																																																			|
% 220.31/171.04  																																																																																			| Instantiating formula (28) with xn, all_903_2_444, 0 and discharging atoms aNaturalNumber0(xn) = all_903_2_444, aNaturalNumber0(xn) = 0, yields:
% 220.31/171.04  																																																																																			| (1928) all_903_2_444 = 0
% 220.31/171.04  																																																																																			|
% 220.31/171.04  																																																																																			| From (1927) and (1920) follows:
% 220.31/171.04  																																																																																			| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.31/171.04  																																																																																			|
% 220.31/171.04  																																																																																			| From (1928) and (1921) follows:
% 220.31/171.04  																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.31/171.04  																																																																																			|
% 220.31/171.04  																																																																																			+-Applying beta-rule and splitting (113), into two cases.
% 220.31/171.04  																																																																																			|-Branch one:
% 220.31/171.04  																																																																																			| (1931) xr = xk
% 220.31/171.04  																																																																																			|
% 220.31/171.04  																																																																																				| From (1931) and (88) follows:
% 220.31/171.04  																																																																																				| (1665) aNaturalNumber0(xk) = 0
% 220.31/171.04  																																																																																				|
% 220.31/171.04  																																																																																				+-Applying beta-rule and splitting (828), into two cases.
% 220.31/171.04  																																																																																				|-Branch one:
% 220.31/171.04  																																																																																				| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 220.31/171.04  																																																																																				|
% 220.31/171.04  																																																																																					| From (1227) and (1933) follows:
% 220.31/171.04  																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.04  																																																																																					|
% 220.31/171.04  																																																																																					| Using (91) and (1934) yields:
% 220.31/171.04  																																																																																					| (1311) $false
% 220.31/171.04  																																																																																					|
% 220.31/171.04  																																																																																					|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																				|-Branch two:
% 220.31/171.04  																																																																																				| (1936) aNaturalNumber0(xn) = all_18_1_20
% 220.31/171.04  																																																																																				| (1227) all_18_1_20 = 0
% 220.31/171.04  																																																																																				|
% 220.31/171.04  																																																																																					| From (1227) and (1936) follows:
% 220.31/171.04  																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.31/171.04  																																																																																					|
% 220.31/171.04  																																																																																					+-Applying beta-rule and splitting (342), into two cases.
% 220.31/171.04  																																																																																					|-Branch one:
% 220.31/171.04  																																																																																					| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 220.31/171.04  																																																																																					|
% 220.31/171.04  																																																																																						| From (1790) and (1939) follows:
% 220.31/171.04  																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.04  																																																																																						|
% 220.31/171.04  																																																																																						| Using (12) and (1940) yields:
% 220.31/171.04  																																																																																						| (1311) $false
% 220.31/171.04  																																																																																						|
% 220.31/171.04  																																																																																						|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																					|-Branch two:
% 220.31/171.04  																																																																																					| (1942) aNaturalNumber0(xm) = all_62_2_94
% 220.31/171.04  																																																																																					| (1790) all_62_2_94 = 0
% 220.31/171.04  																																																																																					|
% 220.31/171.04  																																																																																						| From (1790) and (1942) follows:
% 220.31/171.04  																																																																																						| (12) aNaturalNumber0(xm) = 0
% 220.31/171.04  																																																																																						|
% 220.31/171.04  																																																																																						+-Applying beta-rule and splitting (876), into two cases.
% 220.31/171.04  																																																																																						|-Branch one:
% 220.31/171.04  																																																																																						| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 220.31/171.04  																																																																																						|
% 220.31/171.04  																																																																																							| From (1789) and (1945) follows:
% 220.31/171.04  																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																							| Using (12) and (1940) yields:
% 220.31/171.04  																																																																																							| (1311) $false
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																							|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																						|-Branch two:
% 220.31/171.04  																																																																																						| (1948) aNaturalNumber0(xm) = all_57_2_90
% 220.31/171.04  																																																																																						| (1949) all_57_2_90 = all_14_1_14
% 220.31/171.04  																																																																																						|
% 220.31/171.04  																																																																																							| Combining equations (1789,1949) yields a new equation:
% 220.31/171.04  																																																																																							| (1218) all_14_1_14 = 0
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																							| Combining equations (1218,1949) yields a new equation:
% 220.31/171.04  																																																																																							| (1789) all_57_2_90 = 0
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																							| From (1789) and (1948) follows:
% 220.31/171.04  																																																																																							| (12) aNaturalNumber0(xm) = 0
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																							+-Applying beta-rule and splitting (1035), into two cases.
% 220.31/171.04  																																																																																							|-Branch one:
% 220.31/171.04  																																																																																							| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																								| From (1294) and (1953) follows:
% 220.31/171.04  																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																								| Using (91) and (1934) yields:
% 220.31/171.04  																																																																																								| (1311) $false
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																								|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																							|-Branch two:
% 220.31/171.04  																																																																																							| (1956) aNaturalNumber0(xn) = all_77_2_105
% 220.31/171.04  																																																																																							| (1957) all_77_2_105 = all_37_4_65
% 220.31/171.04  																																																																																							|
% 220.31/171.04  																																																																																								| Combining equations (1294,1957) yields a new equation:
% 220.31/171.04  																																																																																								| (1232) all_37_4_65 = 0
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																								| Combining equations (1232,1957) yields a new equation:
% 220.31/171.04  																																																																																								| (1294) all_77_2_105 = 0
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																								| From (1294) and (1956) follows:
% 220.31/171.04  																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																								+-Applying beta-rule and splitting (976), into two cases.
% 220.31/171.04  																																																																																								|-Branch one:
% 220.31/171.04  																																																																																								| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																									| From (1227) and (1933) follows:
% 220.31/171.04  																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																									| Using (91) and (1934) yields:
% 220.31/171.04  																																																																																									| (1311) $false
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																									|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																								|-Branch two:
% 220.31/171.04  																																																																																								| (1936) aNaturalNumber0(xn) = all_18_1_20
% 220.31/171.04  																																																																																								| (1965) all_62_1_93 = all_18_1_20
% 220.31/171.04  																																																																																								|
% 220.31/171.04  																																																																																									| Combining equations (1240,1965) yields a new equation:
% 220.31/171.04  																																																																																									| (1227) all_18_1_20 = 0
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																									| Combining equations (1227,1965) yields a new equation:
% 220.31/171.04  																																																																																									| (1240) all_62_1_93 = 0
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																									| From (1227) and (1936) follows:
% 220.31/171.04  																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																									+-Applying beta-rule and splitting (808), into two cases.
% 220.31/171.04  																																																																																									|-Branch one:
% 220.31/171.04  																																																																																									| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																										| From (1281) and (1969) follows:
% 220.31/171.04  																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.04  																																																																																										|
% 220.31/171.04  																																																																																										| Using (12) and (1940) yields:
% 220.31/171.04  																																																																																										| (1311) $false
% 220.31/171.04  																																																																																										|
% 220.31/171.04  																																																																																										|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																									|-Branch two:
% 220.31/171.04  																																																																																									| (1972) aNaturalNumber0(xm) = all_12_0_10
% 220.31/171.04  																																																																																									| (1973) all_22_1_26 = all_12_0_10
% 220.31/171.04  																																																																																									|
% 220.31/171.04  																																																																																										| Combining equations (1229,1973) yields a new equation:
% 220.31/171.04  																																																																																										| (1281) all_12_0_10 = 0
% 220.31/171.04  																																																																																										|
% 220.31/171.04  																																																																																										| Combining equations (1281,1973) yields a new equation:
% 220.31/171.04  																																																																																										| (1229) all_22_1_26 = 0
% 220.31/171.04  																																																																																										|
% 220.31/171.04  																																																																																										| From (1281) and (1972) follows:
% 220.31/171.04  																																																																																										| (12) aNaturalNumber0(xm) = 0
% 220.31/171.04  																																																																																										|
% 220.31/171.04  																																																																																										+-Applying beta-rule and splitting (874), into two cases.
% 220.31/171.04  																																																																																										|-Branch one:
% 220.31/171.04  																																																																																										| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 220.31/171.04  																																																																																										|
% 220.31/171.04  																																																																																											| From (1791) and (1977) follows:
% 220.31/171.04  																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.04  																																																																																											|
% 220.31/171.04  																																																																																											| Using (12) and (1940) yields:
% 220.31/171.04  																																																																																											| (1311) $false
% 220.31/171.04  																																																																																											|
% 220.31/171.04  																																																																																											|-The branch is then unsatisfiable
% 220.31/171.04  																																																																																										|-Branch two:
% 220.31/171.05  																																																																																										| (1980) aNaturalNumber0(xm) = all_72_2_101
% 220.31/171.05  																																																																																										| (1981) all_72_2_101 = all_14_1_14
% 220.31/171.05  																																																																																										|
% 220.31/171.05  																																																																																											| Combining equations (1791,1981) yields a new equation:
% 220.31/171.05  																																																																																											| (1218) all_14_1_14 = 0
% 220.31/171.05  																																																																																											|
% 220.31/171.05  																																																																																											| Combining equations (1218,1981) yields a new equation:
% 220.31/171.05  																																																																																											| (1791) all_72_2_101 = 0
% 220.31/171.05  																																																																																											|
% 220.31/171.05  																																																																																											| From (1791) and (1980) follows:
% 220.31/171.05  																																																																																											| (12) aNaturalNumber0(xm) = 0
% 220.31/171.05  																																																																																											|
% 220.31/171.05  																																																																																											+-Applying beta-rule and splitting (989), into two cases.
% 220.31/171.05  																																																																																											|-Branch one:
% 220.31/171.05  																																																																																											| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 220.31/171.05  																																																																																											|
% 220.31/171.05  																																																																																												| From (1350) and (1985) follows:
% 220.31/171.05  																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																												| Using (91) and (1934) yields:
% 220.31/171.05  																																																																																												| (1311) $false
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																												|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																											|-Branch two:
% 220.31/171.05  																																																																																											| (1988) aNaturalNumber0(xn) = all_24_0_28
% 220.31/171.05  																																																																																											| (1989) all_57_1_89 = all_24_0_28
% 220.31/171.05  																																																																																											|
% 220.31/171.05  																																																																																												| Combining equations (980,1989) yields a new equation:
% 220.31/171.05  																																																																																												| (1350) all_24_0_28 = 0
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																												| Combining equations (1350,1989) yields a new equation:
% 220.31/171.05  																																																																																												| (980) all_57_1_89 = 0
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																												| From (1350) and (1988) follows:
% 220.31/171.05  																																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																												+-Applying beta-rule and splitting (319), into two cases.
% 220.31/171.05  																																																																																												|-Branch one:
% 220.31/171.05  																																																																																												| (1993)  ~ (aNaturalNumber0(sz10) = all_67_2_97)
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																													| From (1829) and (1993) follows:
% 220.31/171.05  																																																																																													| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.31/171.05  																																																																																													|
% 220.31/171.05  																																																																																													| Using (61) and (1994) yields:
% 220.31/171.05  																																																																																													| (1311) $false
% 220.31/171.05  																																																																																													|
% 220.31/171.05  																																																																																													|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																												|-Branch two:
% 220.31/171.05  																																																																																												| (1996) aNaturalNumber0(sz10) = all_67_2_97
% 220.31/171.05  																																																																																												| (1829) all_67_2_97 = 0
% 220.31/171.05  																																																																																												|
% 220.31/171.05  																																																																																													| From (1829) and (1996) follows:
% 220.31/171.05  																																																																																													| (61) aNaturalNumber0(sz10) = 0
% 220.31/171.05  																																																																																													|
% 220.31/171.05  																																																																																													+-Applying beta-rule and splitting (964), into two cases.
% 220.31/171.05  																																																																																													|-Branch one:
% 220.31/171.05  																																																																																													| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 220.31/171.05  																																																																																													|
% 220.31/171.05  																																																																																														| From (1350) and (1985) follows:
% 220.31/171.05  																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																														| Using (91) and (1934) yields:
% 220.31/171.05  																																																																																														| (1311) $false
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																														|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																													|-Branch two:
% 220.31/171.05  																																																																																													| (1988) aNaturalNumber0(xn) = all_24_0_28
% 220.31/171.05  																																																																																													| (2003) all_62_1_93 = all_24_0_28
% 220.31/171.05  																																																																																													|
% 220.31/171.05  																																																																																														| Combining equations (1240,2003) yields a new equation:
% 220.31/171.05  																																																																																														| (1350) all_24_0_28 = 0
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																														| Combining equations (1350,2003) yields a new equation:
% 220.31/171.05  																																																																																														| (1240) all_62_1_93 = 0
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																														| From (1350) and (1988) follows:
% 220.31/171.05  																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																														+-Applying beta-rule and splitting (578), into two cases.
% 220.31/171.05  																																																																																														|-Branch one:
% 220.31/171.05  																																																																																														| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																															| From (1283) and (2007) follows:
% 220.31/171.05  																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																															| Using (9) and (2008) yields:
% 220.31/171.05  																																																																																															| (1311) $false
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																															|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																														|-Branch two:
% 220.31/171.05  																																																																																														| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.31/171.05  																																																																																														| (2011) all_67_3_98 = all_26_2_33
% 220.31/171.05  																																																																																														|
% 220.31/171.05  																																																																																															| Combining equations (1241,2011) yields a new equation:
% 220.31/171.05  																																																																																															| (1283) all_26_2_33 = 0
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																															| Combining equations (1283,2011) yields a new equation:
% 220.31/171.05  																																																																																															| (1241) all_67_3_98 = 0
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																															| From (1283) and (2010) follows:
% 220.31/171.05  																																																																																															| (9) aNaturalNumber0(xp) = 0
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																															+-Applying beta-rule and splitting (897), into two cases.
% 220.31/171.05  																																																																																															|-Branch one:
% 220.31/171.05  																																																																																															| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																																| From (1789) and (1945) follows:
% 220.31/171.05  																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																| Using (12) and (1940) yields:
% 220.31/171.05  																																																																																																| (1311) $false
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																															|-Branch two:
% 220.31/171.05  																																																																																															| (1948) aNaturalNumber0(xm) = all_57_2_90
% 220.31/171.05  																																																																																															| (2019) all_57_2_90 = all_12_1_11
% 220.31/171.05  																																																																																															|
% 220.31/171.05  																																																																																																| Combining equations (1789,2019) yields a new equation:
% 220.31/171.05  																																																																																																| (1221) all_12_1_11 = 0
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																| Combining equations (1221,2019) yields a new equation:
% 220.31/171.05  																																																																																																| (1789) all_57_2_90 = 0
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																| From (1789) and (1948) follows:
% 220.31/171.05  																																																																																																| (12) aNaturalNumber0(xm) = 0
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																+-Applying beta-rule and splitting (544), into two cases.
% 220.31/171.05  																																																																																																|-Branch one:
% 220.31/171.05  																																																																																																| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																	| From (1292) and (2023) follows:
% 220.31/171.05  																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																	| Using (9) and (2008) yields:
% 220.31/171.05  																																																																																																	| (1311) $false
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																	|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																																|-Branch two:
% 220.31/171.05  																																																																																																| (2026) aNaturalNumber0(xp) = all_16_0_16
% 220.31/171.05  																																																																																																| (2027) all_77_3_106 = all_16_0_16
% 220.31/171.05  																																																																																																|
% 220.31/171.05  																																																																																																	| Combining equations (1245,2027) yields a new equation:
% 220.31/171.05  																																																																																																	| (1292) all_16_0_16 = 0
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																	| Combining equations (1292,2027) yields a new equation:
% 220.31/171.05  																																																																																																	| (1245) all_77_3_106 = 0
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																	| From (1292) and (2026) follows:
% 220.31/171.05  																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																	+-Applying beta-rule and splitting (557), into two cases.
% 220.31/171.05  																																																																																																	|-Branch one:
% 220.31/171.05  																																																																																																	| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																		| From (1787) and (2031) follows:
% 220.31/171.05  																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																		| Using (9) and (2008) yields:
% 220.31/171.05  																																																																																																		| (1311) $false
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																		|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																																	|-Branch two:
% 220.31/171.05  																																																																																																	| (2034) aNaturalNumber0(xp) = all_20_2_24
% 220.31/171.05  																																																																																																	| (2035) all_72_3_102 = all_20_2_24
% 220.31/171.05  																																																																																																	|
% 220.31/171.05  																																																																																																		| Combining equations (1243,2035) yields a new equation:
% 220.31/171.05  																																																																																																		| (1787) all_20_2_24 = 0
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																		| Combining equations (1787,2035) yields a new equation:
% 220.31/171.05  																																																																																																		| (1243) all_72_3_102 = 0
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																		| From (1787) and (2034) follows:
% 220.31/171.05  																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																		+-Applying beta-rule and splitting (677), into two cases.
% 220.31/171.05  																																																																																																		|-Branch one:
% 220.31/171.05  																																																																																																		| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																			| From (1281) and (2039) follows:
% 220.31/171.05  																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																			| Using (9) and (2008) yields:
% 220.31/171.05  																																																																																																			| (1311) $false
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																			|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																																		|-Branch two:
% 220.31/171.05  																																																																																																		| (2042) aNaturalNumber0(xp) = all_12_0_10
% 220.31/171.05  																																																																																																		| (2043) all_26_1_32 = all_12_0_10
% 220.31/171.05  																																																																																																		|
% 220.31/171.05  																																																																																																			| Combining equations (1202,2043) yields a new equation:
% 220.31/171.05  																																																																																																			| (1281) all_12_0_10 = 0
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																			| Combining equations (1281,2043) yields a new equation:
% 220.31/171.05  																																																																																																			| (1202) all_26_1_32 = 0
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																			| From (1281) and (2042) follows:
% 220.31/171.05  																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																			+-Applying beta-rule and splitting (644), into two cases.
% 220.31/171.05  																																																																																																			|-Branch one:
% 220.31/171.05  																																																																																																			| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																				| From (1281) and (2039) follows:
% 220.31/171.05  																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.05  																																																																																																				|
% 220.31/171.05  																																																																																																				| Using (9) and (2008) yields:
% 220.31/171.05  																																																																																																				| (1311) $false
% 220.31/171.05  																																																																																																				|
% 220.31/171.05  																																																																																																				|-The branch is then unsatisfiable
% 220.31/171.05  																																																																																																			|-Branch two:
% 220.31/171.05  																																																																																																			| (2042) aNaturalNumber0(xp) = all_12_0_10
% 220.31/171.05  																																																																																																			| (2051) all_39_6_72 = all_12_0_10
% 220.31/171.05  																																																																																																			|
% 220.31/171.05  																																																																																																				| Combining equations (629,2051) yields a new equation:
% 220.31/171.05  																																																																																																				| (1281) all_12_0_10 = 0
% 220.31/171.05  																																																																																																				|
% 220.31/171.05  																																																																																																				| Combining equations (1281,2051) yields a new equation:
% 220.31/171.05  																																																																																																				| (629) all_39_6_72 = 0
% 220.31/171.05  																																																																																																				|
% 220.31/171.05  																																																																																																				| From (1281) and (2042) follows:
% 220.31/171.05  																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 220.31/171.05  																																																																																																				|
% 220.31/171.05  																																																																																																				+-Applying beta-rule and splitting (811), into two cases.
% 220.31/171.05  																																																																																																				|-Branch one:
% 220.31/171.05  																																																																																																				| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 220.31/171.06  																																																																																																				|
% 220.31/171.06  																																																																																																					| From (1228) and (2055) follows:
% 220.31/171.06  																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.06  																																																																																																					|
% 220.31/171.06  																																																																																																					| Using (91) and (1934) yields:
% 220.31/171.06  																																																																																																					| (1311) $false
% 220.31/171.06  																																																																																																					|
% 220.31/171.06  																																																																																																					|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																				|-Branch two:
% 220.31/171.06  																																																																																																				| (2058) aNaturalNumber0(xn) = all_20_1_23
% 220.31/171.06  																																																																																																				| (1228) all_20_1_23 = 0
% 220.31/171.06  																																																																																																				|
% 220.31/171.06  																																																																																																					| From (1228) and (2058) follows:
% 220.31/171.06  																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.31/171.06  																																																																																																					|
% 220.31/171.06  																																																																																																					+-Applying beta-rule and splitting (938), into two cases.
% 220.31/171.06  																																																																																																					|-Branch one:
% 220.31/171.06  																																																																																																					| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 220.31/171.06  																																																																																																					|
% 220.31/171.06  																																																																																																						| From (1293) and (2061) follows:
% 220.31/171.06  																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																						| Using (91) and (1934) yields:
% 220.31/171.06  																																																																																																						| (1311) $false
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																						|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																					|-Branch two:
% 220.31/171.06  																																																																																																					| (2064) aNaturalNumber0(xn) = all_47_2_83
% 220.31/171.06  																																																																																																					| (2065) all_77_1_104 = all_47_2_83
% 220.31/171.06  																																																																																																					|
% 220.31/171.06  																																																																																																						| Combining equations (1246,2065) yields a new equation:
% 220.31/171.06  																																																																																																						| (1293) all_47_2_83 = 0
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																						| Combining equations (1293,2065) yields a new equation:
% 220.31/171.06  																																																																																																						| (1246) all_77_1_104 = 0
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																						| From (1293) and (2064) follows:
% 220.31/171.06  																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																						+-Applying beta-rule and splitting (414), into two cases.
% 220.31/171.06  																																																																																																						|-Branch one:
% 220.31/171.06  																																																																																																						| (2069)  ~ (aNaturalNumber0(sz00) = all_16_0_16)
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																							| From (1292) and (2069) follows:
% 220.31/171.06  																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.31/171.06  																																																																																																							|
% 220.31/171.06  																																																																																																							| Using (26) and (2070) yields:
% 220.31/171.06  																																																																																																							| (1311) $false
% 220.31/171.06  																																																																																																							|
% 220.31/171.06  																																																																																																							|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																						|-Branch two:
% 220.31/171.06  																																																																																																						| (2072) aNaturalNumber0(sz00) = all_16_0_16
% 220.31/171.06  																																																																																																						| (1292) all_16_0_16 = 0
% 220.31/171.06  																																																																																																						|
% 220.31/171.06  																																																																																																							| From (1292) and (2072) follows:
% 220.31/171.06  																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 220.31/171.06  																																																																																																							|
% 220.31/171.06  																																																																																																							+-Applying beta-rule and splitting (752), into two cases.
% 220.31/171.06  																																																																																																							|-Branch one:
% 220.31/171.06  																																																																																																							| (2075)  ~ (aNaturalNumber0(sz10) = all_39_7_73)
% 220.31/171.06  																																																																																																							|
% 220.31/171.06  																																																																																																								| From (1236) and (2075) follows:
% 220.31/171.06  																																																																																																								| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.31/171.06  																																																																																																								|
% 220.31/171.06  																																																																																																								| Using (61) and (1994) yields:
% 220.31/171.06  																																																																																																								| (1311) $false
% 220.31/171.06  																																																																																																								|
% 220.31/171.06  																																																																																																								|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																							|-Branch two:
% 220.31/171.06  																																																																																																							| (2078) aNaturalNumber0(sz10) = all_39_7_73
% 220.31/171.06  																																																																																																							| (1236) all_39_7_73 = 0
% 220.31/171.06  																																																																																																							|
% 220.31/171.06  																																																																																																								| From (1236) and (2078) follows:
% 220.31/171.06  																																																																																																								| (61) aNaturalNumber0(sz10) = 0
% 220.31/171.06  																																																																																																								|
% 220.31/171.06  																																																																																																								+-Applying beta-rule and splitting (1029), into two cases.
% 220.31/171.06  																																																																																																								|-Branch one:
% 220.31/171.06  																																																																																																								| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 220.31/171.06  																																																																																																								|
% 220.31/171.06  																																																																																																									| From (1221) and (2081) follows:
% 220.31/171.06  																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																									| Using (91) and (1934) yields:
% 220.31/171.06  																																																																																																									| (1311) $false
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																									|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																								|-Branch two:
% 220.31/171.06  																																																																																																								| (2084) aNaturalNumber0(xn) = all_12_1_11
% 220.31/171.06  																																																																																																								| (2085) all_39_8_74 = all_12_1_11
% 220.31/171.06  																																																																																																								|
% 220.31/171.06  																																																																																																									| Combining equations (1179,2085) yields a new equation:
% 220.31/171.06  																																																																																																									| (1221) all_12_1_11 = 0
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																									| Combining equations (1221,2085) yields a new equation:
% 220.31/171.06  																																																																																																									| (1179) all_39_8_74 = 0
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																									| From (1221) and (2084) follows:
% 220.31/171.06  																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																									+-Applying beta-rule and splitting (498), into two cases.
% 220.31/171.06  																																																																																																									|-Branch one:
% 220.31/171.06  																																																																																																									| (2089)  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																										| From (1292) and (2089) follows:
% 220.31/171.06  																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																										| Using (1284) and (2090) yields:
% 220.31/171.06  																																																																																																										| (1311) $false
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																										|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																									|-Branch two:
% 220.31/171.06  																																																																																																									| (2092) aNaturalNumber0(all_0_9_9) = all_16_0_16
% 220.31/171.06  																																																																																																									| (2093) all_16_0_16 = all_12_0_10
% 220.31/171.06  																																																																																																									|
% 220.31/171.06  																																																																																																										| Combining equations (1292,2093) yields a new equation:
% 220.31/171.06  																																																																																																										| (1281) all_12_0_10 = 0
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																										| Combining equations (1281,2093) yields a new equation:
% 220.31/171.06  																																																																																																										| (1292) all_16_0_16 = 0
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																										| From (1292) and (2092) follows:
% 220.31/171.06  																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																										+-Applying beta-rule and splitting (892), into two cases.
% 220.31/171.06  																																																																																																										|-Branch one:
% 220.31/171.06  																																																																																																										| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																											| From (1830) and (2097) follows:
% 220.31/171.06  																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																											| Using (12) and (1940) yields:
% 220.31/171.06  																																																																																																											| (1311) $false
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																											|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																										|-Branch two:
% 220.31/171.06  																																																																																																										| (2100) aNaturalNumber0(xm) = all_82_2_109
% 220.31/171.06  																																																																																																										| (2101) all_82_2_109 = all_12_1_11
% 220.31/171.06  																																																																																																										|
% 220.31/171.06  																																																																																																											| Combining equations (1830,2101) yields a new equation:
% 220.31/171.06  																																																																																																											| (1221) all_12_1_11 = 0
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																											| Combining equations (1221,2101) yields a new equation:
% 220.31/171.06  																																																																																																											| (1830) all_82_2_109 = 0
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																											| From (1830) and (2100) follows:
% 220.31/171.06  																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																											+-Applying beta-rule and splitting (540), into two cases.
% 220.31/171.06  																																																																																																											|-Branch one:
% 220.31/171.06  																																																																																																											| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																												| From (1788) and (2105) follows:
% 220.31/171.06  																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.06  																																																																																																												|
% 220.31/171.06  																																																																																																												| Using (9) and (2008) yields:
% 220.31/171.06  																																																																																																												| (1311) $false
% 220.31/171.06  																																																																																																												|
% 220.31/171.06  																																																																																																												|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																											|-Branch two:
% 220.31/171.06  																																																																																																											| (2108) aNaturalNumber0(xp) = all_22_2_27
% 220.31/171.06  																																																																																																											| (2109) all_77_3_106 = all_22_2_27
% 220.31/171.06  																																																																																																											|
% 220.31/171.06  																																																																																																												| Combining equations (1245,2109) yields a new equation:
% 220.31/171.06  																																																																																																												| (1788) all_22_2_27 = 0
% 220.31/171.06  																																																																																																												|
% 220.31/171.06  																																																																																																												| From (1788) and (2108) follows:
% 220.31/171.06  																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 220.31/171.06  																																																																																																												|
% 220.31/171.06  																																																																																																												+-Applying beta-rule and splitting (534), into two cases.
% 220.31/171.06  																																																																																																												|-Branch one:
% 220.31/171.06  																																																																																																												| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 220.31/171.06  																																																																																																												|
% 220.31/171.06  																																																																																																													| From (1830) and (2112) follows:
% 220.31/171.06  																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																													| Using (9) and (2008) yields:
% 220.31/171.06  																																																																																																													| (1311) $false
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																													|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																												|-Branch two:
% 220.31/171.06  																																																																																																												| (2115) aNaturalNumber0(xp) = all_82_2_109
% 220.31/171.06  																																																																																																												| (2116) all_82_2_109 = all_77_3_106
% 220.31/171.06  																																																																																																												|
% 220.31/171.06  																																																																																																													| Combining equations (1830,2116) yields a new equation:
% 220.31/171.06  																																																																																																													| (1245) all_77_3_106 = 0
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																													| Combining equations (1245,2116) yields a new equation:
% 220.31/171.06  																																																																																																													| (1830) all_82_2_109 = 0
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																													| From (1830) and (2115) follows:
% 220.31/171.06  																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																													+-Applying beta-rule and splitting (1107), into two cases.
% 220.31/171.06  																																																																																																													|-Branch one:
% 220.31/171.06  																																																																																																													| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																														| From (1829) and (2120) follows:
% 220.31/171.06  																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.06  																																																																																																														|
% 220.31/171.06  																																																																																																														| Using (91) and (1934) yields:
% 220.31/171.06  																																																																																																														| (1311) $false
% 220.31/171.06  																																																																																																														|
% 220.31/171.06  																																																																																																														|-The branch is then unsatisfiable
% 220.31/171.06  																																																																																																													|-Branch two:
% 220.31/171.06  																																																																																																													| (2123) aNaturalNumber0(xn) = all_67_2_97
% 220.31/171.06  																																																																																																													| (2124) all_67_2_97 = all_14_2_15
% 220.31/171.06  																																																																																																													|
% 220.31/171.06  																																																																																																														| Combining equations (1829,2124) yields a new equation:
% 220.31/171.06  																																																																																																														| (1200) all_14_2_15 = 0
% 220.31/171.06  																																																																																																														|
% 220.31/171.06  																																																																																																														| Combining equations (1200,2124) yields a new equation:
% 220.31/171.06  																																																																																																														| (1829) all_67_2_97 = 0
% 220.31/171.06  																																																																																																														|
% 220.31/171.06  																																																																																																														| From (1829) and (2123) follows:
% 220.31/171.06  																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.31/171.06  																																																																																																														|
% 220.31/171.06  																																																																																																														+-Applying beta-rule and splitting (388), into two cases.
% 220.31/171.06  																																																																																																														|-Branch one:
% 220.31/171.06  																																																																																																														| (2128)  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 220.31/171.07  																																																																																																														|
% 220.31/171.07  																																																																																																															| From (1828) and (2128) follows:
% 220.31/171.07  																																																																																																															| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																															| Using (1295) and (2129) yields:
% 220.31/171.07  																																																																																																															| (1311) $false
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																															|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																														|-Branch two:
% 220.31/171.07  																																																																																																														| (2131) aNaturalNumber0(all_0_7_7) = all_20_0_22
% 220.31/171.07  																																																																																																														| (2132) all_77_2_105 = all_20_0_22
% 220.31/171.07  																																																																																																														|
% 220.31/171.07  																																																																																																															| Combining equations (1294,2132) yields a new equation:
% 220.31/171.07  																																																																																																															| (1828) all_20_0_22 = 0
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																															| Combining equations (1828,2132) yields a new equation:
% 220.31/171.07  																																																																																																															| (1294) all_77_2_105 = 0
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																															| From (1828) and (2131) follows:
% 220.31/171.07  																																																																																																															| (1295) aNaturalNumber0(all_0_7_7) = 0
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																															+-Applying beta-rule and splitting (842), into two cases.
% 220.31/171.07  																																																																																																															|-Branch one:
% 220.31/171.07  																																																																																																															| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																																| From (1350) and (2136) follows:
% 220.31/171.07  																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																| Using (12) and (1940) yields:
% 220.31/171.07  																																																																																																																| (1311) $false
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																															|-Branch two:
% 220.31/171.07  																																																																																																															| (2139) aNaturalNumber0(xm) = all_24_0_28
% 220.31/171.07  																																																																																																															| (2140) all_24_0_28 = all_18_1_20
% 220.31/171.07  																																																																																																															|
% 220.31/171.07  																																																																																																																| Combining equations (1350,2140) yields a new equation:
% 220.31/171.07  																																																																																																																| (1227) all_18_1_20 = 0
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																| Combining equations (1227,2140) yields a new equation:
% 220.31/171.07  																																																																																																																| (1350) all_24_0_28 = 0
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																| From (1350) and (2139) follows:
% 220.31/171.07  																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																+-Applying beta-rule and splitting (801), into two cases.
% 220.31/171.07  																																																																																																																|-Branch one:
% 220.31/171.07  																																																																																																																| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																	| From (1788) and (2144) follows:
% 220.31/171.07  																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.07  																																																																																																																	|
% 220.31/171.07  																																																																																																																	| Using (12) and (1940) yields:
% 220.31/171.07  																																																																																																																	| (1311) $false
% 220.31/171.07  																																																																																																																	|
% 220.31/171.07  																																																																																																																	|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																|-Branch two:
% 220.31/171.07  																																																																																																																| (2147) aNaturalNumber0(xm) = all_22_2_27
% 220.31/171.07  																																																																																																																| (2148) all_22_1_26 = all_22_2_27
% 220.31/171.07  																																																																																																																|
% 220.31/171.07  																																																																																																																	| Combining equations (1229,2148) yields a new equation:
% 220.31/171.07  																																																																																																																	| (1788) all_22_2_27 = 0
% 220.31/171.07  																																																																																																																	|
% 220.31/171.07  																																																																																																																	| From (1788) and (2147) follows:
% 220.31/171.07  																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 220.31/171.07  																																																																																																																	|
% 220.31/171.07  																																																																																																																	+-Applying beta-rule and splitting (1106), into two cases.
% 220.31/171.07  																																																																																																																	|-Branch one:
% 220.31/171.07  																																																																																																																	| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 220.31/171.07  																																																																																																																	|
% 220.31/171.07  																																																																																																																		| From (1830) and (2151) follows:
% 220.31/171.07  																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																		| Using (91) and (1934) yields:
% 220.31/171.07  																																																																																																																		| (1311) $false
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																		|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																	|-Branch two:
% 220.31/171.07  																																																																																																																	| (2154) aNaturalNumber0(xn) = all_82_2_109
% 220.31/171.07  																																																																																																																	| (2155) all_82_2_109 = all_14_2_15
% 220.31/171.07  																																																																																																																	|
% 220.31/171.07  																																																																																																																		| Combining equations (1830,2155) yields a new equation:
% 220.31/171.07  																																																																																																																		| (1200) all_14_2_15 = 0
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																		| Combining equations (1200,2155) yields a new equation:
% 220.31/171.07  																																																																																																																		| (1830) all_82_2_109 = 0
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																		| From (1830) and (2154) follows:
% 220.31/171.07  																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																		+-Applying beta-rule and splitting (395), into two cases.
% 220.31/171.07  																																																																																																																		|-Branch one:
% 220.31/171.07  																																																																																																																		| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																			| From (1293) and (2159) follows:
% 220.31/171.07  																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.07  																																																																																																																			|
% 220.31/171.07  																																																																																																																			| Using (9) and (2008) yields:
% 220.31/171.07  																																																																																																																			| (1311) $false
% 220.31/171.07  																																																																																																																			|
% 220.31/171.07  																																																																																																																			|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																		|-Branch two:
% 220.31/171.07  																																																																																																																		| (2162) aNaturalNumber0(xp) = all_47_2_83
% 220.31/171.07  																																																																																																																		| (1293) all_47_2_83 = 0
% 220.31/171.07  																																																																																																																		|
% 220.31/171.07  																																																																																																																			| From (1293) and (2162) follows:
% 220.31/171.07  																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 220.31/171.07  																																																																																																																			|
% 220.31/171.07  																																																																																																																			+-Applying beta-rule and splitting (813), into two cases.
% 220.31/171.07  																																																																																																																			|-Branch one:
% 220.31/171.07  																																																																																																																			| (2165)  ~ (aNaturalNumber0(sz00) = all_20_1_23)
% 220.31/171.07  																																																																																																																			|
% 220.31/171.07  																																																																																																																				| From (1228) and (2165) follows:
% 220.31/171.07  																																																																																																																				| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.31/171.07  																																																																																																																				|
% 220.31/171.07  																																																																																																																				| Using (26) and (2070) yields:
% 220.31/171.07  																																																																																																																				| (1311) $false
% 220.31/171.07  																																																																																																																				|
% 220.31/171.07  																																																																																																																				|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																			|-Branch two:
% 220.31/171.07  																																																																																																																			| (2168) aNaturalNumber0(sz00) = all_20_1_23
% 220.31/171.07  																																																																																																																			| (1228) all_20_1_23 = 0
% 220.31/171.07  																																																																																																																			|
% 220.31/171.07  																																																																																																																				| From (1228) and (2168) follows:
% 220.31/171.07  																																																																																																																				| (26) aNaturalNumber0(sz00) = 0
% 220.31/171.07  																																																																																																																				|
% 220.31/171.07  																																																																																																																				+-Applying beta-rule and splitting (647), into two cases.
% 220.31/171.07  																																																																																																																				|-Branch one:
% 220.31/171.07  																																																																																																																				| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 220.31/171.07  																																																																																																																				|
% 220.31/171.07  																																																																																																																					| From (1828) and (2171) follows:
% 220.31/171.07  																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.07  																																																																																																																					|
% 220.31/171.07  																																																																																																																					| Using (9) and (2008) yields:
% 220.31/171.07  																																																																																																																					| (1311) $false
% 220.31/171.07  																																																																																																																					|
% 220.31/171.07  																																																																																																																					|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																				|-Branch two:
% 220.31/171.07  																																																																																																																				| (2174) aNaturalNumber0(xp) = all_20_0_22
% 220.31/171.07  																																																																																																																				| (2175) all_37_2_63 = all_20_0_22
% 220.31/171.07  																																																																																																																				|
% 220.31/171.07  																																																																																																																					| Combining equations (1195,2175) yields a new equation:
% 220.31/171.07  																																																																																																																					| (1828) all_20_0_22 = 0
% 220.31/171.07  																																																																																																																					|
% 220.31/171.07  																																																																																																																					| From (1828) and (2174) follows:
% 220.31/171.07  																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 220.31/171.07  																																																																																																																					|
% 220.31/171.07  																																																																																																																					+-Applying beta-rule and splitting (470), into two cases.
% 220.31/171.07  																																																																																																																					|-Branch one:
% 220.31/171.07  																																																																																																																					| (2178)  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 220.31/171.07  																																																																																																																					|
% 220.31/171.07  																																																																																																																						| From (1828) and (2178) follows:
% 220.31/171.07  																																																																																																																						| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																						| Using (1284) and (2090) yields:
% 220.31/171.07  																																																																																																																						| (1311) $false
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																						|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																					|-Branch two:
% 220.31/171.07  																																																																																																																					| (2181) aNaturalNumber0(all_0_9_9) = all_20_0_22
% 220.31/171.07  																																																																																																																					| (2182) all_24_2_30 = all_20_0_22
% 220.31/171.07  																																																																																																																					|
% 220.31/171.07  																																																																																																																						| Combining equations (1282,2182) yields a new equation:
% 220.31/171.07  																																																																																																																						| (1828) all_20_0_22 = 0
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																						| Combining equations (1828,2182) yields a new equation:
% 220.31/171.07  																																																																																																																						| (1282) all_24_2_30 = 0
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																						| From (1828) and (2181) follows:
% 220.31/171.07  																																																																																																																						| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																						+-Applying beta-rule and splitting (618), into two cases.
% 220.31/171.07  																																																																																																																						|-Branch one:
% 220.31/171.07  																																																																																																																						| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																							| From (1789) and (2186) follows:
% 220.31/171.07  																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.07  																																																																																																																							|
% 220.31/171.07  																																																																																																																							| Using (9) and (2008) yields:
% 220.31/171.07  																																																																																																																							| (1311) $false
% 220.31/171.07  																																																																																																																							|
% 220.31/171.07  																																																																																																																							|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																						|-Branch two:
% 220.31/171.07  																																																																																																																						| (2189) aNaturalNumber0(xp) = all_57_2_90
% 220.31/171.07  																																																																																																																						| (2190) all_57_2_90 = all_47_3_84
% 220.31/171.07  																																																																																																																						|
% 220.31/171.07  																																																																																																																							| Combining equations (1789,2190) yields a new equation:
% 220.31/171.07  																																																																																																																							| (2191) all_47_3_84 = 0
% 220.31/171.07  																																																																																																																							|
% 220.31/171.07  																																																																																																																							| Combining equations (2191,2190) yields a new equation:
% 220.31/171.07  																																																																																																																							| (1789) all_57_2_90 = 0
% 220.31/171.07  																																																																																																																							|
% 220.31/171.07  																																																																																																																							| From (1789) and (2189) follows:
% 220.31/171.07  																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 220.31/171.07  																																																																																																																							|
% 220.31/171.07  																																																																																																																							+-Applying beta-rule and splitting (587), into two cases.
% 220.31/171.07  																																																																																																																							|-Branch one:
% 220.31/171.07  																																																																																																																							| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 220.31/171.07  																																																																																																																							|
% 220.31/171.07  																																																																																																																								| From (1789) and (2186) follows:
% 220.31/171.07  																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.07  																																																																																																																								|
% 220.31/171.07  																																																																																																																								| Using (9) and (2008) yields:
% 220.31/171.07  																																																																																																																								| (1311) $false
% 220.31/171.07  																																																																																																																								|
% 220.31/171.07  																																																																																																																								|-The branch is then unsatisfiable
% 220.31/171.07  																																																																																																																							|-Branch two:
% 220.31/171.08  																																																																																																																							| (2189) aNaturalNumber0(xp) = all_57_2_90
% 220.31/171.08  																																																																																																																							| (2198) all_57_2_90 = all_57_3_91
% 220.31/171.08  																																																																																																																							|
% 220.31/171.08  																																																																																																																								| Combining equations (1789,2198) yields a new equation:
% 220.31/171.08  																																																																																																																								| (2199) all_57_3_91 = 0
% 220.31/171.08  																																																																																																																								|
% 220.31/171.08  																																																																																																																								| Combining equations (2199,2198) yields a new equation:
% 220.31/171.08  																																																																																																																								| (1789) all_57_2_90 = 0
% 220.31/171.08  																																																																																																																								|
% 220.31/171.08  																																																																																																																								| From (1789) and (2189) follows:
% 220.31/171.08  																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 220.31/171.08  																																																																																																																								|
% 220.31/171.08  																																																																																																																								+-Applying beta-rule and splitting (509), into two cases.
% 220.31/171.08  																																																																																																																								|-Branch one:
% 220.31/171.08  																																																																																																																								| (2202)  ~ (aNaturalNumber0(xk) = all_57_2_90)
% 220.31/171.08  																																																																																																																								|
% 220.31/171.08  																																																																																																																									| From (1789) and (2202) follows:
% 220.31/171.08  																																																																																																																									| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																									| Using (1665) and (1670) yields:
% 220.31/171.08  																																																																																																																									| (1311) $false
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																									|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																								|-Branch two:
% 220.31/171.08  																																																																																																																								| (2205) aNaturalNumber0(xk) = all_57_2_90
% 220.31/171.08  																																																																																																																								| (2206) all_57_2_90 = all_52_2_87
% 220.31/171.08  																																																																																																																								|
% 220.31/171.08  																																																																																																																									| Combining equations (1789,2206) yields a new equation:
% 220.31/171.08  																																																																																																																									| (1674) all_52_2_87 = 0
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																									| Combining equations (1674,2206) yields a new equation:
% 220.31/171.08  																																																																																																																									| (1789) all_57_2_90 = 0
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																									| From (1789) and (2205) follows:
% 220.31/171.08  																																																																																																																									| (1665) aNaturalNumber0(xk) = 0
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																									+-Applying beta-rule and splitting (1114), into two cases.
% 220.31/171.08  																																																																																																																									|-Branch one:
% 220.31/171.08  																																																																																																																									| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																										| From (1282) and (2210) follows:
% 220.31/171.08  																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																										| Using (91) and (1934) yields:
% 220.31/171.08  																																																																																																																										| (1311) $false
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																										|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																									|-Branch two:
% 220.31/171.08  																																																																																																																									| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.31/171.08  																																																																																																																									| (2214) all_24_2_30 = all_14_2_15
% 220.31/171.08  																																																																																																																									|
% 220.31/171.08  																																																																																																																										| Combining equations (1282,2214) yields a new equation:
% 220.31/171.08  																																																																																																																										| (1200) all_14_2_15 = 0
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																										| Combining equations (1200,2214) yields a new equation:
% 220.31/171.08  																																																																																																																										| (1282) all_24_2_30 = 0
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																										| From (1282) and (2213) follows:
% 220.31/171.08  																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																										+-Applying beta-rule and splitting (495), into two cases.
% 220.31/171.08  																																																																																																																										|-Branch one:
% 220.31/171.08  																																																																																																																										| (2218)  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																											| From (1787) and (2218) follows:
% 220.31/171.08  																																																																																																																											| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																											| Using (1284) and (2090) yields:
% 220.31/171.08  																																																																																																																											| (1311) $false
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																											|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																										|-Branch two:
% 220.31/171.08  																																																																																																																										| (2221) aNaturalNumber0(all_0_9_9) = all_20_2_24
% 220.31/171.08  																																																																																																																										| (2222) all_20_2_24 = all_12_0_10
% 220.31/171.08  																																																																																																																										|
% 220.31/171.08  																																																																																																																											| Combining equations (1787,2222) yields a new equation:
% 220.31/171.08  																																																																																																																											| (1281) all_12_0_10 = 0
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																											| Combining equations (1281,2222) yields a new equation:
% 220.31/171.08  																																																																																																																											| (1787) all_20_2_24 = 0
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																											| From (1787) and (2221) follows:
% 220.31/171.08  																																																																																																																											| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																											+-Applying beta-rule and splitting (481), into two cases.
% 220.31/171.08  																																																																																																																											|-Branch one:
% 220.31/171.08  																																																																																																																											| (2226)  ~ (aNaturalNumber0(xr) = all_12_0_10)
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																												| From (1931)(1281) and (2226) follows:
% 220.31/171.08  																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.31/171.08  																																																																																																																												|
% 220.31/171.08  																																																																																																																												| Using (1665) and (1670) yields:
% 220.31/171.08  																																																																																																																												| (1311) $false
% 220.31/171.08  																																																																																																																												|
% 220.31/171.08  																																																																																																																												|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																											|-Branch two:
% 220.31/171.08  																																																																																																																											| (2229) aNaturalNumber0(xr) = all_12_0_10
% 220.31/171.08  																																																																																																																											| (1281) all_12_0_10 = 0
% 220.31/171.08  																																																																																																																											|
% 220.31/171.08  																																																																																																																												| From (1931)(1281) and (2229) follows:
% 220.31/171.08  																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 220.31/171.08  																																																																																																																												|
% 220.31/171.08  																																																																																																																												+-Applying beta-rule and splitting (479), into two cases.
% 220.31/171.08  																																																																																																																												|-Branch one:
% 220.31/171.08  																																																																																																																												| (2232)  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 220.31/171.08  																																																																																																																												|
% 220.31/171.08  																																																																																																																													| From (1350) and (2232) follows:
% 220.31/171.08  																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																													| Using (1284) and (2090) yields:
% 220.31/171.08  																																																																																																																													| (1311) $false
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																													|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																												|-Branch two:
% 220.31/171.08  																																																																																																																												| (2235) aNaturalNumber0(all_0_9_9) = all_24_0_28
% 220.31/171.08  																																																																																																																												| (2236) all_24_0_28 = all_24_2_30
% 220.31/171.08  																																																																																																																												|
% 220.31/171.08  																																																																																																																													| Combining equations (1350,2236) yields a new equation:
% 220.31/171.08  																																																																																																																													| (1282) all_24_2_30 = 0
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																													| Combining equations (1282,2236) yields a new equation:
% 220.31/171.08  																																																																																																																													| (1350) all_24_0_28 = 0
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																													| From (1350) and (2235) follows:
% 220.31/171.08  																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																													+-Applying beta-rule and splitting (812), into two cases.
% 220.31/171.08  																																																																																																																													|-Branch one:
% 220.31/171.08  																																																																																																																													| (2240)  ~ (aNaturalNumber0(sz10) = all_20_1_23)
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																														| From (1228) and (2240) follows:
% 220.31/171.08  																																																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.31/171.08  																																																																																																																														|
% 220.31/171.08  																																																																																																																														| Using (61) and (1994) yields:
% 220.31/171.08  																																																																																																																														| (1311) $false
% 220.31/171.08  																																																																																																																														|
% 220.31/171.08  																																																																																																																														|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																													|-Branch two:
% 220.31/171.08  																																																																																																																													| (2243) aNaturalNumber0(sz10) = all_20_1_23
% 220.31/171.08  																																																																																																																													| (1228) all_20_1_23 = 0
% 220.31/171.08  																																																																																																																													|
% 220.31/171.08  																																																																																																																														| From (1228) and (2243) follows:
% 220.31/171.08  																																																																																																																														| (61) aNaturalNumber0(sz10) = 0
% 220.31/171.08  																																																																																																																														|
% 220.31/171.08  																																																																																																																														+-Applying beta-rule and splitting (344), into two cases.
% 220.31/171.08  																																																																																																																														|-Branch one:
% 220.31/171.08  																																																																																																																														| (2246)  ~ (aNaturalNumber0(sz00) = all_62_2_94)
% 220.31/171.08  																																																																																																																														|
% 220.31/171.08  																																																																																																																															| From (1790) and (2246) follows:
% 220.31/171.08  																																																																																																																															| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.31/171.08  																																																																																																																															|
% 220.31/171.08  																																																																																																																															| Using (26) and (2070) yields:
% 220.31/171.08  																																																																																																																															| (1311) $false
% 220.31/171.08  																																																																																																																															|
% 220.31/171.08  																																																																																																																															|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																														|-Branch two:
% 220.31/171.08  																																																																																																																														| (2249) aNaturalNumber0(sz00) = all_62_2_94
% 220.31/171.08  																																																																																																																														| (1790) all_62_2_94 = 0
% 220.31/171.08  																																																																																																																														|
% 220.31/171.08  																																																																																																																															| From (1790) and (2249) follows:
% 220.31/171.08  																																																																																																																															| (26) aNaturalNumber0(sz00) = 0
% 220.31/171.08  																																																																																																																															|
% 220.31/171.08  																																																																																																																															+-Applying beta-rule and splitting (1063), into two cases.
% 220.31/171.08  																																																																																																																															|-Branch one:
% 220.31/171.08  																																																																																																																															| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 220.31/171.08  																																																																																																																															|
% 220.31/171.08  																																																																																																																																| From (1283) and (2252) follows:
% 220.31/171.08  																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.08  																																																																																																																																|
% 220.31/171.08  																																																																																																																																| Using (91) and (1934) yields:
% 220.31/171.08  																																																																																																																																| (1311) $false
% 220.31/171.08  																																																																																																																																|
% 220.31/171.08  																																																																																																																																|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																															|-Branch two:
% 220.31/171.08  																																																																																																																															| (2255) aNaturalNumber0(xn) = all_26_2_33
% 220.31/171.08  																																																																																																																															| (2256) all_26_2_33 = all_18_2_21
% 220.31/171.08  																																																																																																																															|
% 220.31/171.08  																																																																																																																																| Combining equations (1283,2256) yields a new equation:
% 220.31/171.08  																																																																																																																																| (1226) all_18_2_21 = 0
% 220.31/171.08  																																																																																																																																|
% 220.31/171.08  																																																																																																																																| Combining equations (1226,2256) yields a new equation:
% 220.31/171.08  																																																																																																																																| (1283) all_26_2_33 = 0
% 220.31/171.08  																																																																																																																																|
% 220.31/171.08  																																																																																																																																| From (1283) and (2255) follows:
% 220.31/171.08  																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 220.31/171.08  																																																																																																																																|
% 220.31/171.08  																																																																																																																																+-Applying beta-rule and splitting (529), into two cases.
% 220.31/171.08  																																																																																																																																|-Branch one:
% 220.31/171.08  																																																																																																																																| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 220.31/171.08  																																																																																																																																|
% 220.31/171.08  																																																																																																																																	| From (1292) and (2023) follows:
% 220.31/171.08  																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.08  																																																																																																																																	|
% 220.31/171.08  																																																																																																																																	| Using (9) and (2008) yields:
% 220.31/171.08  																																																																																																																																	| (1311) $false
% 220.31/171.08  																																																																																																																																	|
% 220.31/171.08  																																																																																																																																	|-The branch is then unsatisfiable
% 220.31/171.08  																																																																																																																																|-Branch two:
% 220.31/171.09  																																																																																																																																| (2026) aNaturalNumber0(xp) = all_16_0_16
% 220.31/171.09  																																																																																																																																| (2264) all_82_3_110 = all_16_0_16
% 220.31/171.09  																																																																																																																																|
% 220.31/171.09  																																																																																																																																	| Combining equations (1247,2264) yields a new equation:
% 220.31/171.09  																																																																																																																																	| (1292) all_16_0_16 = 0
% 220.31/171.09  																																																																																																																																	|
% 220.31/171.09  																																																																																																																																	| Combining equations (1292,2264) yields a new equation:
% 220.31/171.09  																																																																																																																																	| (1247) all_82_3_110 = 0
% 220.31/171.09  																																																																																																																																	|
% 220.31/171.09  																																																																																																																																	| From (1292) and (2026) follows:
% 220.31/171.09  																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 220.31/171.09  																																																																																																																																	|
% 220.31/171.09  																																																																																																																																	+-Applying beta-rule and splitting (1027), into two cases.
% 220.31/171.09  																																																																																																																																	|-Branch one:
% 220.31/171.09  																																																																																																																																	| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 220.31/171.09  																																																																																																																																	|
% 220.31/171.09  																																																																																																																																		| From (848) and (2268) follows:
% 220.31/171.09  																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.09  																																																																																																																																		|
% 220.31/171.09  																																																																																																																																		| Using (91) and (1934) yields:
% 220.31/171.09  																																																																																																																																		| (1311) $false
% 220.31/171.09  																																																																																																																																		|
% 220.31/171.09  																																																																																																																																		|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																	|-Branch two:
% 220.31/171.09  																																																																																																																																	| (2271) aNaturalNumber0(xn) = all_16_1_17
% 220.31/171.09  																																																																																																																																	| (2272) all_39_8_74 = all_16_1_17
% 220.31/171.09  																																																																																																																																	|
% 220.31/171.09  																																																																																																																																		| Combining equations (1179,2272) yields a new equation:
% 220.31/171.09  																																																																																																																																		| (848) all_16_1_17 = 0
% 220.31/171.09  																																																																																																																																		|
% 220.31/171.09  																																																																																																																																		| From (848) and (2271) follows:
% 220.31/171.09  																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 220.31/171.09  																																																																																																																																		|
% 220.31/171.09  																																																																																																																																		+-Applying beta-rule and splitting (822), into two cases.
% 220.31/171.09  																																																																																																																																		|-Branch one:
% 220.31/171.09  																																																																																																																																		| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 220.31/171.09  																																																																																																																																		|
% 220.31/171.09  																																																																																																																																			| From (1294) and (2275) follows:
% 220.31/171.09  																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																			| Using (12) and (1940) yields:
% 220.31/171.09  																																																																																																																																			| (1311) $false
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																			|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																		|-Branch two:
% 220.31/171.09  																																																																																																																																		| (2278) aNaturalNumber0(xm) = all_77_2_105
% 220.31/171.09  																																																																																																																																		| (2279) all_77_2_105 = all_20_1_23
% 220.31/171.09  																																																																																																																																		|
% 220.31/171.09  																																																																																																																																			| Combining equations (1294,2279) yields a new equation:
% 220.31/171.09  																																																																																																																																			| (1228) all_20_1_23 = 0
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																			| Combining equations (1228,2279) yields a new equation:
% 220.31/171.09  																																																																																																																																			| (1294) all_77_2_105 = 0
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																			| From (1294) and (2278) follows:
% 220.31/171.09  																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																			+-Applying beta-rule and splitting (686), into two cases.
% 220.31/171.09  																																																																																																																																			|-Branch one:
% 220.31/171.09  																																																																																																																																			| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																				| From (1787) and (2031) follows:
% 220.31/171.09  																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.31/171.09  																																																																																																																																				|
% 220.31/171.09  																																																																																																																																				| Using (9) and (2008) yields:
% 220.31/171.09  																																																																																																																																				| (1311) $false
% 220.31/171.09  																																																																																																																																				|
% 220.31/171.09  																																																																																																																																				|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																			|-Branch two:
% 220.31/171.09  																																																																																																																																			| (2034) aNaturalNumber0(xp) = all_20_2_24
% 220.31/171.09  																																																																																																																																			| (2287) all_24_1_29 = all_20_2_24
% 220.31/171.09  																																																																																																																																			|
% 220.31/171.09  																																																																																																																																				| Combining equations (1207,2287) yields a new equation:
% 220.31/171.09  																																																																																																																																				| (1787) all_20_2_24 = 0
% 220.31/171.09  																																																																																																																																				|
% 220.31/171.09  																																																																																																																																				| From (1787) and (2034) follows:
% 220.31/171.09  																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 220.31/171.09  																																																																																																																																				|
% 220.31/171.09  																																																																																																																																				+-Applying beta-rule and splitting (449), into two cases.
% 220.31/171.09  																																																																																																																																				|-Branch one:
% 220.31/171.09  																																																																																																																																				| (2290)  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 220.31/171.09  																																																																																																																																				|
% 220.31/171.09  																																																																																																																																					| From (1830) and (2290) follows:
% 220.31/171.09  																																																																																																																																					| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																					| Using (1284) and (2090) yields:
% 220.31/171.09  																																																																																																																																					| (1311) $false
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																					|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																				|-Branch two:
% 220.31/171.09  																																																																																																																																				| (2293) aNaturalNumber0(all_0_9_9) = all_82_2_109
% 220.31/171.09  																																																																																																																																				| (2294) all_82_2_109 = all_26_2_33
% 220.31/171.09  																																																																																																																																				|
% 220.31/171.09  																																																																																																																																					| Combining equations (1830,2294) yields a new equation:
% 220.31/171.09  																																																																																																																																					| (1283) all_26_2_33 = 0
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																					| Combining equations (1283,2294) yields a new equation:
% 220.31/171.09  																																																																																																																																					| (1830) all_82_2_109 = 0
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																					| From (1830) and (2293) follows:
% 220.31/171.09  																																																																																																																																					| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																					+-Applying beta-rule and splitting (756), into two cases.
% 220.31/171.09  																																																																																																																																					|-Branch one:
% 220.31/171.09  																																																																																																																																					| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																						| From (1828) and (2298) follows:
% 220.31/171.09  																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																						| Using (12) and (1940) yields:
% 220.31/171.09  																																																																																																																																						| (1311) $false
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																						|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																					|-Branch two:
% 220.31/171.09  																																																																																																																																					| (2301) aNaturalNumber0(xm) = all_20_0_22
% 220.31/171.09  																																																																																																																																					| (2302) all_39_7_73 = all_20_0_22
% 220.31/171.09  																																																																																																																																					|
% 220.31/171.09  																																																																																																																																						| Combining equations (1236,2302) yields a new equation:
% 220.31/171.09  																																																																																																																																						| (1828) all_20_0_22 = 0
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																						| Combining equations (1828,2302) yields a new equation:
% 220.31/171.09  																																																																																																																																						| (1236) all_39_7_73 = 0
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																						| From (1828) and (2301) follows:
% 220.31/171.09  																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																						+-Applying beta-rule and splitting (313), into two cases.
% 220.31/171.09  																																																																																																																																						|-Branch one:
% 220.31/171.09  																																																																																																																																						| (2306)  ~ (aNaturalNumber0(sz00) = all_82_2_109)
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																							| From (1830) and (2306) follows:
% 220.31/171.09  																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.31/171.09  																																																																																																																																							|
% 220.31/171.09  																																																																																																																																							| Using (26) and (2070) yields:
% 220.31/171.09  																																																																																																																																							| (1311) $false
% 220.31/171.09  																																																																																																																																							|
% 220.31/171.09  																																																																																																																																							|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																						|-Branch two:
% 220.31/171.09  																																																																																																																																						| (2309) aNaturalNumber0(sz00) = all_82_2_109
% 220.31/171.09  																																																																																																																																						| (1830) all_82_2_109 = 0
% 220.31/171.09  																																																																																																																																						|
% 220.31/171.09  																																																																																																																																							| From (1830) and (2309) follows:
% 220.31/171.09  																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 220.31/171.09  																																																																																																																																							|
% 220.31/171.09  																																																																																																																																							+-Applying beta-rule and splitting (455), into two cases.
% 220.31/171.09  																																																																																																																																							|-Branch one:
% 220.31/171.09  																																																																																																																																							| (2312)  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 220.31/171.09  																																																																																																																																							|
% 220.31/171.09  																																																																																																																																								| From (1788) and (2312) follows:
% 220.31/171.09  																																																																																																																																								| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																								| Using (1284) and (2090) yields:
% 220.31/171.09  																																																																																																																																								| (1311) $false
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																								|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																							|-Branch two:
% 220.31/171.09  																																																																																																																																							| (2315) aNaturalNumber0(all_0_9_9) = all_22_2_27
% 220.31/171.09  																																																																																																																																							| (2316) all_26_2_33 = all_22_2_27
% 220.31/171.09  																																																																																																																																							|
% 220.31/171.09  																																																																																																																																								| Combining equations (1283,2316) yields a new equation:
% 220.31/171.09  																																																																																																																																								| (1788) all_22_2_27 = 0
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																								| Combining equations (1788,2316) yields a new equation:
% 220.31/171.09  																																																																																																																																								| (1283) all_26_2_33 = 0
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																								| From (1788) and (2315) follows:
% 220.31/171.09  																																																																																																																																								| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																								+-Applying beta-rule and splitting (933), into two cases.
% 220.31/171.09  																																																																																																																																								|-Branch one:
% 220.31/171.09  																																																																																																																																								| (2320)  ~ (aNaturalNumber0(sz00) = all_77_1_104)
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																									| From (1246) and (2320) follows:
% 220.31/171.09  																																																																																																																																									| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.31/171.09  																																																																																																																																									|
% 220.31/171.09  																																																																																																																																									| Using (26) and (2070) yields:
% 220.31/171.09  																																																																																																																																									| (1311) $false
% 220.31/171.09  																																																																																																																																									|
% 220.31/171.09  																																																																																																																																									|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																								|-Branch two:
% 220.31/171.09  																																																																																																																																								| (2323) aNaturalNumber0(sz00) = all_77_1_104
% 220.31/171.09  																																																																																																																																								| (1246) all_77_1_104 = 0
% 220.31/171.09  																																																																																																																																								|
% 220.31/171.09  																																																																																																																																									| From (1246) and (2323) follows:
% 220.31/171.09  																																																																																																																																									| (26) aNaturalNumber0(sz00) = 0
% 220.31/171.09  																																																																																																																																									|
% 220.31/171.09  																																																																																																																																									+-Applying beta-rule and splitting (496), into two cases.
% 220.31/171.09  																																																																																																																																									|-Branch one:
% 220.31/171.09  																																																																																																																																									| (2326)  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 220.31/171.09  																																																																																																																																									|
% 220.31/171.09  																																																																																																																																										| From (1294) and (2326) follows:
% 220.31/171.09  																																																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.31/171.09  																																																																																																																																										|
% 220.31/171.09  																																																																																																																																										| Using (1284) and (2090) yields:
% 220.31/171.09  																																																																																																																																										| (1311) $false
% 220.31/171.09  																																																																																																																																										|
% 220.31/171.09  																																																																																																																																										|-The branch is then unsatisfiable
% 220.31/171.09  																																																																																																																																									|-Branch two:
% 220.31/171.09  																																																																																																																																									| (2329) aNaturalNumber0(all_0_9_9) = all_77_2_105
% 220.31/171.09  																																																																																																																																									| (2330) all_77_2_105 = all_12_0_10
% 220.31/171.09  																																																																																																																																									|
% 220.31/171.09  																																																																																																																																										| Combining equations (1294,2330) yields a new equation:
% 220.31/171.09  																																																																																																																																										| (1281) all_12_0_10 = 0
% 220.31/171.09  																																																																																																																																										|
% 220.31/171.09  																																																																																																																																										| Combining equations (1281,2330) yields a new equation:
% 220.31/171.09  																																																																																																																																										| (1294) all_77_2_105 = 0
% 220.31/171.09  																																																																																																																																										|
% 220.31/171.09  																																																																																																																																										| From (1294) and (2329) follows:
% 220.31/171.09  																																																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.31/171.09  																																																																																																																																										|
% 220.31/171.09  																																																																																																																																										+-Applying beta-rule and splitting (1143), into two cases.
% 220.31/171.09  																																																																																																																																										|-Branch one:
% 220.31/171.09  																																																																																																																																										| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 220.31/171.09  																																																																																																																																										|
% 220.31/171.09  																																																																																																																																											| From (1242) and (2334) follows:
% 220.31/171.10  																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.10  																																																																																																																																											|
% 220.31/171.10  																																																																																																																																											| Using (91) and (1934) yields:
% 220.31/171.10  																																																																																																																																											| (1311) $false
% 220.31/171.10  																																																																																																																																											|
% 220.31/171.10  																																																																																																																																											|-The branch is then unsatisfiable
% 220.31/171.10  																																																																																																																																										|-Branch two:
% 220.31/171.10  																																																																																																																																										| (2337) aNaturalNumber0(xn) = all_67_1_96
% 220.31/171.10  																																																																																																																																										| (2338) all_67_1_96 = all_12_2_12
% 220.31/171.10  																																																																																																																																										|
% 220.31/171.10  																																																																																																																																											| Combining equations (1242,2338) yields a new equation:
% 220.31/171.10  																																																																																																																																											| (1223) all_12_2_12 = 0
% 220.31/171.10  																																																																																																																																											|
% 220.31/171.10  																																																																																																																																											| Combining equations (1223,2338) yields a new equation:
% 220.31/171.10  																																																																																																																																											| (1242) all_67_1_96 = 0
% 220.31/171.10  																																																																																																																																											|
% 220.31/171.10  																																																																																																																																											| From (1242) and (2337) follows:
% 220.31/171.10  																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 220.31/171.10  																																																																																																																																											|
% 220.31/171.10  																																																																																																																																											+-Applying beta-rule and splitting (1009), into two cases.
% 220.31/171.10  																																																																																																																																											|-Branch one:
% 220.31/171.10  																																																																																																																																											| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 220.31/171.10  																																																																																																																																											|
% 220.31/171.10  																																																																																																																																												| From (1829) and (2120) follows:
% 220.31/171.10  																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.31/171.10  																																																																																																																																												|
% 220.31/171.10  																																																																																																																																												| Using (91) and (1934) yields:
% 220.31/171.10  																																																																																																																																												| (1311) $false
% 220.31/171.10  																																																																																																																																												|
% 220.63/171.10  																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																											|-Branch two:
% 220.63/171.10  																																																																																																																																											| (2123) aNaturalNumber0(xn) = all_67_2_97
% 220.63/171.10  																																																																																																																																											| (2346) all_67_2_97 = all_39_8_74
% 220.63/171.10  																																																																																																																																											|
% 220.63/171.10  																																																																																																																																												| Combining equations (1829,2346) yields a new equation:
% 220.63/171.10  																																																																																																																																												| (1179) all_39_8_74 = 0
% 220.63/171.10  																																																																																																																																												|
% 220.63/171.10  																																																																																																																																												| Combining equations (1179,2346) yields a new equation:
% 220.63/171.10  																																																																																																																																												| (1829) all_67_2_97 = 0
% 220.63/171.10  																																																																																																																																												|
% 220.63/171.10  																																																																																																																																												| From (1829) and (2123) follows:
% 220.63/171.10  																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.63/171.10  																																																																																																																																												|
% 220.63/171.10  																																																																																																																																												+-Applying beta-rule and splitting (965), into two cases.
% 220.63/171.10  																																																																																																																																												|-Branch one:
% 220.63/171.10  																																																																																																																																												| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 220.63/171.10  																																																																																																																																												|
% 220.63/171.10  																																																																																																																																													| From (1283) and (2252) follows:
% 220.63/171.10  																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																													| Using (91) and (1934) yields:
% 220.63/171.10  																																																																																																																																													| (1311) $false
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																												|-Branch two:
% 220.63/171.10  																																																																																																																																												| (2255) aNaturalNumber0(xn) = all_26_2_33
% 220.63/171.10  																																																																																																																																												| (2354) all_62_1_93 = all_26_2_33
% 220.63/171.10  																																																																																																																																												|
% 220.63/171.10  																																																																																																																																													| Combining equations (1240,2354) yields a new equation:
% 220.63/171.10  																																																																																																																																													| (1283) all_26_2_33 = 0
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																													| Combining equations (1283,2354) yields a new equation:
% 220.63/171.10  																																																																																																																																													| (1240) all_62_1_93 = 0
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																													| From (1283) and (2255) follows:
% 220.63/171.10  																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																													+-Applying beta-rule and splitting (1138), into two cases.
% 220.63/171.10  																																																																																																																																													|-Branch one:
% 220.63/171.10  																																																																																																																																													| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																														| From (1283) and (2252) follows:
% 220.63/171.10  																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																														| Using (91) and (1934) yields:
% 220.63/171.10  																																																																																																																																														| (1311) $false
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																													|-Branch two:
% 220.63/171.10  																																																																																																																																													| (2255) aNaturalNumber0(xn) = all_26_2_33
% 220.63/171.10  																																																																																																																																													| (2362) all_26_2_33 = all_12_2_12
% 220.63/171.10  																																																																																																																																													|
% 220.63/171.10  																																																																																																																																														| Combining equations (1283,2362) yields a new equation:
% 220.63/171.10  																																																																																																																																														| (1223) all_12_2_12 = 0
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																														| Combining equations (1223,2362) yields a new equation:
% 220.63/171.10  																																																																																																																																														| (1283) all_26_2_33 = 0
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																														| From (1283) and (2255) follows:
% 220.63/171.10  																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																														+-Applying beta-rule and splitting (704), into two cases.
% 220.63/171.10  																																																																																																																																														|-Branch one:
% 220.63/171.10  																																																																																																																																														| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																															| From (1787) and (2366) follows:
% 220.63/171.10  																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																															| Using (12) and (1940) yields:
% 220.63/171.10  																																																																																																																																															| (1311) $false
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																														|-Branch two:
% 220.63/171.10  																																																																																																																																														| (2369) aNaturalNumber0(xm) = all_20_2_24
% 220.63/171.10  																																																																																																																																														| (2370) all_72_1_100 = all_20_2_24
% 220.63/171.10  																																																																																																																																														|
% 220.63/171.10  																																																																																																																																															| Combining equations (1244,2370) yields a new equation:
% 220.63/171.10  																																																																																																																																															| (1787) all_20_2_24 = 0
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																															| Combining equations (1787,2370) yields a new equation:
% 220.63/171.10  																																																																																																																																															| (1244) all_72_1_100 = 0
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																															| From (1787) and (2369) follows:
% 220.63/171.10  																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																															+-Applying beta-rule and splitting (919), into two cases.
% 220.63/171.10  																																																																																																																																															|-Branch one:
% 220.63/171.10  																																																																																																																																															| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																																| From (1281) and (2374) follows:
% 220.63/171.10  																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																| Using (91) and (1934) yields:
% 220.63/171.10  																																																																																																																																																| (1311) $false
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																															|-Branch two:
% 220.63/171.10  																																																																																																																																															| (2377) aNaturalNumber0(xn) = all_12_0_10
% 220.63/171.10  																																																																																																																																															| (2378) all_82_1_108 = all_12_0_10
% 220.63/171.10  																																																																																																																																															|
% 220.63/171.10  																																																																																																																																																| Combining equations (1249,2378) yields a new equation:
% 220.63/171.10  																																																																																																																																																| (1281) all_12_0_10 = 0
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																| Combining equations (1281,2378) yields a new equation:
% 220.63/171.10  																																																																																																																																																| (1249) all_82_1_108 = 0
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																| From (1281) and (2377) follows:
% 220.63/171.10  																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																+-Applying beta-rule and splitting (767), into two cases.
% 220.63/171.10  																																																																																																																																																|-Branch one:
% 220.63/171.10  																																																																																																																																																| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																	| From (1282) and (2382) follows:
% 220.63/171.10  																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																	| Using (12) and (1940) yields:
% 220.63/171.10  																																																																																																																																																	| (1311) $false
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																																|-Branch two:
% 220.63/171.10  																																																																																																																																																| (2385) aNaturalNumber0(xm) = all_24_2_30
% 220.63/171.10  																																																																																																																																																| (2386) all_39_7_73 = all_24_2_30
% 220.63/171.10  																																																																																																																																																|
% 220.63/171.10  																																																																																																																																																	| Combining equations (1236,2386) yields a new equation:
% 220.63/171.10  																																																																																																																																																	| (1282) all_24_2_30 = 0
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																	| Combining equations (1282,2386) yields a new equation:
% 220.63/171.10  																																																																																																																																																	| (1236) all_39_7_73 = 0
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																	| From (1282) and (2385) follows:
% 220.63/171.10  																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																	+-Applying beta-rule and splitting (934), into two cases.
% 220.63/171.10  																																																																																																																																																	|-Branch one:
% 220.63/171.10  																																																																																																																																																	| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																		| From (1830) and (2151) follows:
% 220.63/171.10  																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																		| Using (91) and (1934) yields:
% 220.63/171.10  																																																																																																																																																		| (1311) $false
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																		|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																																	|-Branch two:
% 220.63/171.10  																																																																																																																																																	| (2154) aNaturalNumber0(xn) = all_82_2_109
% 220.63/171.10  																																																																																																																																																	| (2394) all_82_2_109 = all_77_1_104
% 220.63/171.10  																																																																																																																																																	|
% 220.63/171.10  																																																																																																																																																		| Combining equations (1830,2394) yields a new equation:
% 220.63/171.10  																																																																																																																																																		| (1246) all_77_1_104 = 0
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																		| Combining equations (1246,2394) yields a new equation:
% 220.63/171.10  																																																																																																																																																		| (1830) all_82_2_109 = 0
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																		| From (1830) and (2154) follows:
% 220.63/171.10  																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																		+-Applying beta-rule and splitting (981), into two cases.
% 220.63/171.10  																																																																																																																																																		|-Branch one:
% 220.63/171.10  																																																																																																																																																		| (2398)  ~ (aNaturalNumber0(sz10) = all_57_1_89)
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																			| From (980) and (2398) follows:
% 220.63/171.10  																																																																																																																																																			| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.63/171.10  																																																																																																																																																			|
% 220.63/171.10  																																																																																																																																																			| Using (61) and (1994) yields:
% 220.63/171.10  																																																																																																																																																			| (1311) $false
% 220.63/171.10  																																																																																																																																																			|
% 220.63/171.10  																																																																																																																																																			|-The branch is then unsatisfiable
% 220.63/171.10  																																																																																																																																																		|-Branch two:
% 220.63/171.10  																																																																																																																																																		| (2401) aNaturalNumber0(sz10) = all_57_1_89
% 220.63/171.10  																																																																																																																																																		| (980) all_57_1_89 = 0
% 220.63/171.10  																																																																																																																																																		|
% 220.63/171.10  																																																																																																																																																			| From (980) and (2401) follows:
% 220.63/171.10  																																																																																																																																																			| (61) aNaturalNumber0(sz10) = 0
% 220.63/171.10  																																																																																																																																																			|
% 220.63/171.10  																																																																																																																																																			+-Applying beta-rule and splitting (817), into two cases.
% 220.63/171.10  																																																																																																																																																			|-Branch one:
% 220.63/171.10  																																																																																																																																																			| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 220.63/171.10  																																																																																																																																																			|
% 220.63/171.10  																																																																																																																																																				| From (1791) and (1977) follows:
% 220.63/171.10  																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																				| Using (12) and (1940) yields:
% 220.63/171.11  																																																																																																																																																				| (1311) $false
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																				|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																			|-Branch two:
% 220.63/171.11  																																																																																																																																																			| (1980) aNaturalNumber0(xm) = all_72_2_101
% 220.63/171.11  																																																																																																																																																			| (2408) all_72_2_101 = all_20_1_23
% 220.63/171.11  																																																																																																																																																			|
% 220.63/171.11  																																																																																																																																																				| Combining equations (1791,2408) yields a new equation:
% 220.63/171.11  																																																																																																																																																				| (1228) all_20_1_23 = 0
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																				| Combining equations (1228,2408) yields a new equation:
% 220.63/171.11  																																																																																																																																																				| (1791) all_72_2_101 = 0
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																				| From (1791) and (1980) follows:
% 220.63/171.11  																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																				+-Applying beta-rule and splitting (829), into two cases.
% 220.63/171.11  																																																																																																																																																				|-Branch one:
% 220.63/171.11  																																																																																																																																																				| (2412)  ~ (aNaturalNumber0(sz10) = all_18_1_20)
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																					| From (1227) and (2412) follows:
% 220.63/171.11  																																																																																																																																																					| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.63/171.11  																																																																																																																																																					|
% 220.63/171.11  																																																																																																																																																					| Using (61) and (1994) yields:
% 220.63/171.11  																																																																																																																																																					| (1311) $false
% 220.63/171.11  																																																																																																																																																					|
% 220.63/171.11  																																																																																																																																																					|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																				|-Branch two:
% 220.63/171.11  																																																																																																																																																				| (2415) aNaturalNumber0(sz10) = all_18_1_20
% 220.63/171.11  																																																																																																																																																				| (1227) all_18_1_20 = 0
% 220.63/171.11  																																																																																																																																																				|
% 220.63/171.11  																																																																																																																																																					| From (1227) and (2415) follows:
% 220.63/171.11  																																																																																																																																																					| (61) aNaturalNumber0(sz10) = 0
% 220.63/171.11  																																																																																																																																																					|
% 220.63/171.11  																																																																																																																																																					+-Applying beta-rule and splitting (571), into two cases.
% 220.63/171.11  																																																																																																																																																					|-Branch one:
% 220.63/171.11  																																																																																																																																																					| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 220.63/171.11  																																																																																																																																																					|
% 220.63/171.11  																																																																																																																																																						| From (1789) and (2186) follows:
% 220.63/171.11  																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																						| Using (9) and (2008) yields:
% 220.63/171.11  																																																																																																																																																						| (1311) $false
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																						|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																					|-Branch two:
% 220.63/171.11  																																																																																																																																																					| (2189) aNaturalNumber0(xp) = all_57_2_90
% 220.63/171.11  																																																																																																																																																					| (2422) all_67_3_98 = all_57_2_90
% 220.63/171.11  																																																																																																																																																					|
% 220.63/171.11  																																																																																																																																																						| Combining equations (1241,2422) yields a new equation:
% 220.63/171.11  																																																																																																																																																						| (1789) all_57_2_90 = 0
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																						| Combining equations (1789,2422) yields a new equation:
% 220.63/171.11  																																																																																																																																																						| (1241) all_67_3_98 = 0
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																						| From (1789) and (2189) follows:
% 220.63/171.11  																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																						+-Applying beta-rule and splitting (321), into two cases.
% 220.63/171.11  																																																																																																																																																						|-Branch one:
% 220.63/171.11  																																																																																																																																																						| (2426)  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																							| Using (1831) and (2426) yields:
% 220.63/171.11  																																																																																																																																																							| (1311) $false
% 220.63/171.11  																																																																																																																																																							|
% 220.63/171.11  																																																																																																																																																							|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																						|-Branch two:
% 220.63/171.11  																																																																																																																																																						| (1831) aNaturalNumber0(all_0_2_2) = 0
% 220.63/171.11  																																																																																																																																																						| (1829) all_67_2_97 = 0
% 220.63/171.11  																																																																																																																																																						|
% 220.63/171.11  																																																																																																																																																							+-Applying beta-rule and splitting (941), into two cases.
% 220.63/171.11  																																																																																																																																																							|-Branch one:
% 220.63/171.11  																																																																																																																																																							| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 220.63/171.11  																																																																																																																																																							|
% 220.63/171.11  																																																																																																																																																								| From (1283) and (2252) follows:
% 220.63/171.11  																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																								| Using (91) and (1934) yields:
% 220.63/171.11  																																																																																																																																																								| (1311) $false
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																								|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																							|-Branch two:
% 220.63/171.11  																																																																																																																																																							| (2255) aNaturalNumber0(xn) = all_26_2_33
% 220.63/171.11  																																																																																																																																																							| (2434) all_77_1_104 = all_26_2_33
% 220.63/171.11  																																																																																																																																																							|
% 220.63/171.11  																																																																																																																																																								| Combining equations (1246,2434) yields a new equation:
% 220.63/171.11  																																																																																																																																																								| (1283) all_26_2_33 = 0
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																								| Combining equations (1283,2434) yields a new equation:
% 220.63/171.11  																																																																																																																																																								| (1246) all_77_1_104 = 0
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																								| From (1283) and (2255) follows:
% 220.63/171.11  																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																								+-Applying beta-rule and splitting (592), into two cases.
% 220.63/171.11  																																																																																																																																																								|-Branch one:
% 220.63/171.11  																																																																																																																																																								| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																									| From (1292) and (2023) follows:
% 220.63/171.11  																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																									| Using (9) and (2008) yields:
% 220.63/171.11  																																																																																																																																																									| (1311) $false
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																									|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																								|-Branch two:
% 220.63/171.11  																																																																																																																																																								| (2026) aNaturalNumber0(xp) = all_16_0_16
% 220.63/171.11  																																																																																																																																																								| (2442) all_57_3_91 = all_16_0_16
% 220.63/171.11  																																																																																																																																																								|
% 220.63/171.11  																																																																																																																																																									| Combining equations (2199,2442) yields a new equation:
% 220.63/171.11  																																																																																																																																																									| (1292) all_16_0_16 = 0
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																									| Combining equations (1292,2442) yields a new equation:
% 220.63/171.11  																																																																																																																																																									| (2199) all_57_3_91 = 0
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																									| From (1292) and (2026) follows:
% 220.63/171.11  																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																									+-Applying beta-rule and splitting (1083), into two cases.
% 220.63/171.11  																																																																																																																																																									|-Branch one:
% 220.63/171.11  																																																																																																																																																									| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																										| From (1828) and (2446) follows:
% 220.63/171.11  																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																										| Using (91) and (1934) yields:
% 220.63/171.11  																																																																																																																																																										| (1311) $false
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																										|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																									|-Branch two:
% 220.63/171.11  																																																																																																																																																									| (2449) aNaturalNumber0(xn) = all_20_0_22
% 220.63/171.11  																																																																																																																																																									| (2450) all_20_0_22 = all_16_2_18
% 220.63/171.11  																																																																																																																																																									|
% 220.63/171.11  																																																																																																																																																										| Combining equations (1828,2450) yields a new equation:
% 220.63/171.11  																																																																																																																																																										| (1225) all_16_2_18 = 0
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																										| Combining equations (1225,2450) yields a new equation:
% 220.63/171.11  																																																																																																																																																										| (1828) all_20_0_22 = 0
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																										| From (1828) and (2449) follows:
% 220.63/171.11  																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																										+-Applying beta-rule and splitting (483), into two cases.
% 220.63/171.11  																																																																																																																																																										|-Branch one:
% 220.63/171.11  																																																																																																																																																										| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																											| From (1281) and (1969) follows:
% 220.63/171.11  																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.11  																																																																																																																																																											|
% 220.63/171.11  																																																																																																																																																											| Using (12) and (1940) yields:
% 220.63/171.11  																																																																																																																																																											| (1311) $false
% 220.63/171.11  																																																																																																																																																											|
% 220.63/171.11  																																																																																																																																																											|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																										|-Branch two:
% 220.63/171.11  																																																																																																																																																										| (1972) aNaturalNumber0(xm) = all_12_0_10
% 220.63/171.11  																																																																																																																																																										| (1281) all_12_0_10 = 0
% 220.63/171.11  																																																																																																																																																										|
% 220.63/171.11  																																																																																																																																																											| From (1281) and (1972) follows:
% 220.63/171.11  																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 220.63/171.11  																																																																																																																																																											|
% 220.63/171.11  																																																																																																																																																											+-Applying beta-rule and splitting (1076), into two cases.
% 220.63/171.11  																																																																																																																																																											|-Branch one:
% 220.63/171.11  																																																																																																																																																											| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 220.63/171.11  																																																																																																																																																											|
% 220.63/171.11  																																																																																																																																																												| From (1221) and (2081) follows:
% 220.63/171.11  																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.11  																																																																																																																																																												|
% 220.63/171.11  																																																																																																																																																												| Using (91) and (1934) yields:
% 220.63/171.11  																																																																																																																																																												| (1311) $false
% 220.63/171.11  																																																																																																																																																												|
% 220.63/171.11  																																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																											|-Branch two:
% 220.63/171.11  																																																																																																																																																											| (2084) aNaturalNumber0(xn) = all_12_1_11
% 220.63/171.11  																																																																																																																																																											| (2464) all_18_2_21 = all_12_1_11
% 220.63/171.11  																																																																																																																																																											|
% 220.63/171.11  																																																																																																																																																												| Combining equations (1226,2464) yields a new equation:
% 220.63/171.11  																																																																																																																																																												| (1221) all_12_1_11 = 0
% 220.63/171.11  																																																																																																																																																												|
% 220.63/171.11  																																																																																																																																																												| From (1221) and (2084) follows:
% 220.63/171.11  																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.63/171.11  																																																																																																																																																												|
% 220.63/171.11  																																																																																																																																																												+-Applying beta-rule and splitting (477), into two cases.
% 220.63/171.11  																																																																																																																																																												|-Branch one:
% 220.63/171.11  																																																																																																																																																												| (2467)  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 220.63/171.11  																																																																																																																																																												|
% 220.63/171.11  																																																																																																																																																													| From (1293) and (2467) follows:
% 220.63/171.11  																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.63/171.11  																																																																																																																																																													|
% 220.63/171.11  																																																																																																																																																													| Using (1284) and (2090) yields:
% 220.63/171.11  																																																																																																																																																													| (1311) $false
% 220.63/171.11  																																																																																																																																																													|
% 220.63/171.11  																																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.11  																																																																																																																																																												|-Branch two:
% 220.63/171.11  																																																																																																																																																												| (2470) aNaturalNumber0(all_0_9_9) = all_47_2_83
% 220.63/171.11  																																																																																																																																																												| (2471) all_47_2_83 = all_24_2_30
% 220.63/171.11  																																																																																																																																																												|
% 220.63/171.11  																																																																																																																																																													| Combining equations (1293,2471) yields a new equation:
% 220.63/171.11  																																																																																																																																																													| (1282) all_24_2_30 = 0
% 220.63/171.11  																																																																																																																																																													|
% 220.63/171.11  																																																																																																																																																													| Combining equations (1282,2471) yields a new equation:
% 220.63/171.11  																																																																																																																																																													| (1293) all_47_2_83 = 0
% 220.63/171.11  																																																																																																																																																													|
% 220.63/171.11  																																																																																																																																																													| From (1293) and (2470) follows:
% 220.63/171.12  																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.63/171.12  																																																																																																																																																													|
% 220.63/171.12  																																																																																																																																																													+-Applying beta-rule and splitting (643), into two cases.
% 220.63/171.12  																																																																																																																																																													|-Branch one:
% 220.63/171.12  																																																																																																																																																													| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 220.63/171.12  																																																																																																																																																													|
% 220.63/171.12  																																																																																																																																																														| From (1282) and (2475) follows:
% 220.63/171.12  																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																														| Using (9) and (2008) yields:
% 220.63/171.12  																																																																																																																																																														| (1311) $false
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																													|-Branch two:
% 220.63/171.12  																																																																																																																																																													| (2478) aNaturalNumber0(xp) = all_24_2_30
% 220.63/171.12  																																																																																																																																																													| (2479) all_39_6_72 = all_24_2_30
% 220.63/171.12  																																																																																																																																																													|
% 220.63/171.12  																																																																																																																																																														| Combining equations (629,2479) yields a new equation:
% 220.63/171.12  																																																																																																																																																														| (1282) all_24_2_30 = 0
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																														| Combining equations (1282,2479) yields a new equation:
% 220.63/171.12  																																																																																																																																																														| (629) all_39_6_72 = 0
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																														| From (1282) and (2478) follows:
% 220.63/171.12  																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																														+-Applying beta-rule and splitting (596), into two cases.
% 220.63/171.12  																																																																																																																																																														|-Branch one:
% 220.63/171.12  																																																																																																																																																														| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																															| From (1281) and (2039) follows:
% 220.63/171.12  																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.12  																																																																																																																																																															|
% 220.63/171.12  																																																																																																																																																															| Using (9) and (2008) yields:
% 220.63/171.12  																																																																																																																																																															| (1311) $false
% 220.63/171.12  																																																																																																																																																															|
% 220.63/171.12  																																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																														|-Branch two:
% 220.63/171.12  																																																																																																																																																														| (2042) aNaturalNumber0(xp) = all_12_0_10
% 220.63/171.12  																																																																																																																																																														| (2487) all_57_3_91 = all_12_0_10
% 220.63/171.12  																																																																																																																																																														|
% 220.63/171.12  																																																																																																																																																															| Combining equations (2199,2487) yields a new equation:
% 220.63/171.12  																																																																																																																																																															| (1281) all_12_0_10 = 0
% 220.63/171.12  																																																																																																																																																															|
% 220.63/171.12  																																																																																																																																																															| From (1281) and (2042) follows:
% 220.63/171.12  																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 220.63/171.12  																																																																																																																																																															|
% 220.63/171.12  																																																																																																																																																															+-Applying beta-rule and splitting (971), into two cases.
% 220.63/171.12  																																																																																																																																																															|-Branch one:
% 220.63/171.12  																																																																																																																																																															| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 220.63/171.12  																																																																																																																																																															|
% 220.63/171.12  																																																																																																																																																																| From (1237) and (2490) follows:
% 220.63/171.12  																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																| Using (91) and (1934) yields:
% 220.63/171.12  																																																																																																																																																																| (1311) $false
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																															|-Branch two:
% 220.63/171.12  																																																																																																																																																															| (2493) aNaturalNumber0(xn) = all_47_1_82
% 220.63/171.12  																																																																																																																																																															| (2494) all_62_1_93 = all_47_1_82
% 220.63/171.12  																																																																																																																																																															|
% 220.63/171.12  																																																																																																																																																																| Combining equations (1240,2494) yields a new equation:
% 220.63/171.12  																																																																																																																																																																| (1237) all_47_1_82 = 0
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																| Combining equations (1237,2494) yields a new equation:
% 220.63/171.12  																																																																																																																																																																| (1240) all_62_1_93 = 0
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																| From (1237) and (2493) follows:
% 220.63/171.12  																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																+-Applying beta-rule and splitting (339), into two cases.
% 220.63/171.12  																																																																																																																																																																|-Branch one:
% 220.63/171.12  																																																																																																																																																																| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																	| From (1828) and (2498) follows:
% 220.63/171.12  																																																																																																																																																																	| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																	| Using (1775) and (1780) yields:
% 220.63/171.12  																																																																																																																																																																	| (1311) $false
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																																|-Branch two:
% 220.63/171.12  																																																																																																																																																																| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 220.63/171.12  																																																																																																																																																																| (2502) all_72_2_101 = all_20_0_22
% 220.63/171.12  																																																																																																																																																																|
% 220.63/171.12  																																																																																																																																																																	| Combining equations (1791,2502) yields a new equation:
% 220.63/171.12  																																																																																																																																																																	| (1828) all_20_0_22 = 0
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																	| Combining equations (1828,2502) yields a new equation:
% 220.63/171.12  																																																																																																																																																																	| (1791) all_72_2_101 = 0
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																	| From (1828) and (2501) follows:
% 220.63/171.12  																																																																																																																																																																	| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																	+-Applying beta-rule and splitting (554), into two cases.
% 220.63/171.12  																																																																																																																																																																	|-Branch one:
% 220.63/171.12  																																																																																																																																																																	| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																		| From (1790) and (2506) follows:
% 220.63/171.12  																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																		| Using (9) and (2008) yields:
% 220.63/171.12  																																																																																																																																																																		| (1311) $false
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																																	|-Branch two:
% 220.63/171.12  																																																																																																																																																																	| (2509) aNaturalNumber0(xp) = all_62_2_94
% 220.63/171.12  																																																																																																																																																																	| (2510) all_72_3_102 = all_62_2_94
% 220.63/171.12  																																																																																																																																																																	|
% 220.63/171.12  																																																																																																																																																																		| Combining equations (1243,2510) yields a new equation:
% 220.63/171.12  																																																																																																																																																																		| (1790) all_62_2_94 = 0
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																		| Combining equations (1790,2510) yields a new equation:
% 220.63/171.12  																																																																																																																																																																		| (1243) all_72_3_102 = 0
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																		| From (1790) and (2509) follows:
% 220.63/171.12  																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																		+-Applying beta-rule and splitting (531), into two cases.
% 220.63/171.12  																																																																																																																																																																		|-Branch one:
% 220.63/171.12  																																																																																																																																																																		| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																			| From (1283) and (2007) follows:
% 220.63/171.12  																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																			| Using (9) and (2008) yields:
% 220.63/171.12  																																																																																																																																																																			| (1311) $false
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																																		|-Branch two:
% 220.63/171.12  																																																																																																																																																																		| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.63/171.12  																																																																																																																																																																		| (2518) all_82_3_110 = all_26_2_33
% 220.63/171.12  																																																																																																																																																																		|
% 220.63/171.12  																																																																																																																																																																			| Combining equations (1247,2518) yields a new equation:
% 220.63/171.12  																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																			| Combining equations (1283,2518) yields a new equation:
% 220.63/171.12  																																																																																																																																																																			| (1247) all_82_3_110 = 0
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																			| From (1283) and (2010) follows:
% 220.63/171.12  																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																			+-Applying beta-rule and splitting (1022), into two cases.
% 220.63/171.12  																																																																																																																																																																			|-Branch one:
% 220.63/171.12  																																																																																																																																																																			| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																				| From (1236) and (2522) follows:
% 220.63/171.12  																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																				| Using (91) and (1934) yields:
% 220.63/171.12  																																																																																																																																																																				| (1311) $false
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																																			|-Branch two:
% 220.63/171.12  																																																																																																																																																																			| (2525) aNaturalNumber0(xn) = all_39_7_73
% 220.63/171.12  																																																																																																																																																																			| (2526) all_39_7_73 = all_39_8_74
% 220.63/171.12  																																																																																																																																																																			|
% 220.63/171.12  																																																																																																																																																																				| Combining equations (1236,2526) yields a new equation:
% 220.63/171.12  																																																																																																																																																																				| (1179) all_39_8_74 = 0
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																				| Combining equations (1179,2526) yields a new equation:
% 220.63/171.12  																																																																																																																																																																				| (1236) all_39_7_73 = 0
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																				| From (1236) and (2525) follows:
% 220.63/171.12  																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																				+-Applying beta-rule and splitting (546), into two cases.
% 220.63/171.12  																																																																																																																																																																				|-Branch one:
% 220.63/171.12  																																																																																																																																																																				| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																					| From (1283) and (2007) follows:
% 220.63/171.12  																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																					| Using (9) and (2008) yields:
% 220.63/171.12  																																																																																																																																																																					| (1311) $false
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																																				|-Branch two:
% 220.63/171.12  																																																																																																																																																																				| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.63/171.12  																																																																																																																																																																				| (2534) all_77_3_106 = all_26_2_33
% 220.63/171.12  																																																																																																																																																																				|
% 220.63/171.12  																																																																																																																																																																					| Combining equations (1245,2534) yields a new equation:
% 220.63/171.12  																																																																																																																																																																					| (1283) all_26_2_33 = 0
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																					| Combining equations (1283,2534) yields a new equation:
% 220.63/171.12  																																																																																																																																																																					| (1245) all_77_3_106 = 0
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																					| From (1283) and (2010) follows:
% 220.63/171.12  																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																					+-Applying beta-rule and splitting (1068), into two cases.
% 220.63/171.12  																																																																																																																																																																					|-Branch one:
% 220.63/171.12  																																																																																																																																																																					| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																						| From (1242) and (2334) follows:
% 220.63/171.12  																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.12  																																																																																																																																																																						|
% 220.63/171.12  																																																																																																																																																																						| Using (91) and (1934) yields:
% 220.63/171.12  																																																																																																																																																																						| (1311) $false
% 220.63/171.12  																																																																																																																																																																						|
% 220.63/171.12  																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.63/171.12  																																																																																																																																																																					|-Branch two:
% 220.63/171.12  																																																																																																																																																																					| (2337) aNaturalNumber0(xn) = all_67_1_96
% 220.63/171.12  																																																																																																																																																																					| (2542) all_67_1_96 = all_18_2_21
% 220.63/171.12  																																																																																																																																																																					|
% 220.63/171.12  																																																																																																																																																																						| Combining equations (1242,2542) yields a new equation:
% 220.63/171.12  																																																																																																																																																																						| (1226) all_18_2_21 = 0
% 220.63/171.12  																																																																																																																																																																						|
% 220.63/171.12  																																																																																																																																																																						| Combining equations (1226,2542) yields a new equation:
% 220.63/171.12  																																																																																																																																																																						| (1242) all_67_1_96 = 0
% 220.63/171.12  																																																																																																																																																																						|
% 220.63/171.12  																																																																																																																																																																						| From (1242) and (2337) follows:
% 220.63/171.13  																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.63/171.13  																																																																																																																																																																						|
% 220.63/171.13  																																																																																																																																																																						+-Applying beta-rule and splitting (851), into two cases.
% 220.63/171.13  																																																																																																																																																																						|-Branch one:
% 220.63/171.13  																																																																																																																																																																						| (2546)  ~ (aNaturalNumber0(sz00) = all_16_1_17)
% 220.63/171.13  																																																																																																																																																																						|
% 220.63/171.13  																																																																																																																																																																							| From (848) and (2546) follows:
% 220.63/171.13  																																																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.63/171.13  																																																																																																																																																																							|
% 220.63/171.13  																																																																																																																																																																							| Using (26) and (2070) yields:
% 220.63/171.13  																																																																																																																																																																							| (1311) $false
% 220.63/171.13  																																																																																																																																																																							|
% 220.63/171.13  																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																						|-Branch two:
% 220.63/171.13  																																																																																																																																																																						| (2549) aNaturalNumber0(sz00) = all_16_1_17
% 220.63/171.13  																																																																																																																																																																						| (848) all_16_1_17 = 0
% 220.63/171.13  																																																																																																																																																																						|
% 220.63/171.13  																																																																																																																																																																							| From (848) and (2549) follows:
% 220.63/171.13  																																																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 220.63/171.13  																																																																																																																																																																							|
% 220.63/171.13  																																																																																																																																																																							+-Applying beta-rule and splitting (503), into two cases.
% 220.63/171.13  																																																																																																																																																																							|-Branch one:
% 220.63/171.13  																																																																																																																																																																							| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 220.63/171.13  																																																																																																																																																																							|
% 220.63/171.13  																																																																																																																																																																								| From (1674) and (2552) follows:
% 220.63/171.13  																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.13  																																																																																																																																																																								|
% 220.63/171.13  																																																																																																																																																																								| Using (91) and (1934) yields:
% 220.63/171.13  																																																																																																																																																																								| (1311) $false
% 220.63/171.13  																																																																																																																																																																								|
% 220.63/171.13  																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																							|-Branch two:
% 220.63/171.13  																																																																																																																																																																							| (2555) aNaturalNumber0(xn) = all_52_2_87
% 220.63/171.13  																																																																																																																																																																							| (1674) all_52_2_87 = 0
% 220.63/171.13  																																																																																																																																																																							|
% 220.63/171.13  																																																																																																																																																																								| From (1674) and (2555) follows:
% 220.63/171.13  																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.63/171.13  																																																																																																																																																																								|
% 220.63/171.13  																																																																																																																																																																								+-Applying beta-rule and splitting (473), into two cases.
% 220.63/171.13  																																																																																																																																																																								|-Branch one:
% 220.63/171.13  																																																																																																																																																																								| (2558)  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 220.63/171.13  																																																																																																																																																																								|
% 220.63/171.13  																																																																																																																																																																									| From (1789) and (2558) follows:
% 220.63/171.13  																																																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																									| Using (1284) and (2090) yields:
% 220.63/171.13  																																																																																																																																																																									| (1311) $false
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																								|-Branch two:
% 220.63/171.13  																																																																																																																																																																								| (2561) aNaturalNumber0(all_0_9_9) = all_57_2_90
% 220.63/171.13  																																																																																																																																																																								| (2562) all_57_2_90 = all_24_2_30
% 220.63/171.13  																																																																																																																																																																								|
% 220.63/171.13  																																																																																																																																																																									| Combining equations (1789,2562) yields a new equation:
% 220.63/171.13  																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																									| Combining equations (1282,2562) yields a new equation:
% 220.63/171.13  																																																																																																																																																																									| (1789) all_57_2_90 = 0
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																									| From (1789) and (2561) follows:
% 220.63/171.13  																																																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																									+-Applying beta-rule and splitting (855), into two cases.
% 220.63/171.13  																																																																																																																																																																									|-Branch one:
% 220.63/171.13  																																																																																																																																																																									| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																										| From (1791) and (1977) follows:
% 220.63/171.13  																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																										| Using (12) and (1940) yields:
% 220.63/171.13  																																																																																																																																																																										| (1311) $false
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																									|-Branch two:
% 220.63/171.13  																																																																																																																																																																									| (1980) aNaturalNumber0(xm) = all_72_2_101
% 220.63/171.13  																																																																																																																																																																									| (2570) all_72_2_101 = all_16_1_17
% 220.63/171.13  																																																																																																																																																																									|
% 220.63/171.13  																																																																																																																																																																										| Combining equations (1791,2570) yields a new equation:
% 220.63/171.13  																																																																																																																																																																										| (848) all_16_1_17 = 0
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																										| Combining equations (848,2570) yields a new equation:
% 220.63/171.13  																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																										| From (1791) and (1980) follows:
% 220.63/171.13  																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																										+-Applying beta-rule and splitting (437), into two cases.
% 220.63/171.13  																																																																																																																																																																										|-Branch one:
% 220.63/171.13  																																																																																																																																																																										| (2574)  ~ (aNaturalNumber0(all_0_8_8) = all_57_2_90)
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																											| From (1789) and (2574) follows:
% 220.63/171.13  																																																																																																																																																																											| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																											| Using (1351) and (2575) yields:
% 220.63/171.13  																																																																																																																																																																											| (1311) $false
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																										|-Branch two:
% 220.63/171.13  																																																																																																																																																																										| (2577) aNaturalNumber0(all_0_8_8) = all_57_2_90
% 220.63/171.13  																																																																																																																																																																										| (2578) all_57_2_90 = all_24_0_28
% 220.63/171.13  																																																																																																																																																																										|
% 220.63/171.13  																																																																																																																																																																											| Combining equations (1789,2578) yields a new equation:
% 220.63/171.13  																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																											| Combining equations (1350,2578) yields a new equation:
% 220.63/171.13  																																																																																																																																																																											| (1789) all_57_2_90 = 0
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																											| From (1789) and (2577) follows:
% 220.63/171.13  																																																																																																																																																																											| (1351) aNaturalNumber0(all_0_8_8) = 0
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																											+-Applying beta-rule and splitting (929), into two cases.
% 220.63/171.13  																																																																																																																																																																											|-Branch one:
% 220.63/171.13  																																																																																																																																																																											| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																												| From (848) and (2268) follows:
% 220.63/171.13  																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																												| Using (91) and (1934) yields:
% 220.63/171.13  																																																																																																																																																																												| (1311) $false
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																											|-Branch two:
% 220.63/171.13  																																																																																																																																																																											| (2271) aNaturalNumber0(xn) = all_16_1_17
% 220.63/171.13  																																																																																																																																																																											| (2586) all_82_1_108 = all_16_1_17
% 220.63/171.13  																																																																																																																																																																											|
% 220.63/171.13  																																																																																																																																																																												| Combining equations (1249,2586) yields a new equation:
% 220.63/171.13  																																																																																																																																																																												| (848) all_16_1_17 = 0
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																												| Combining equations (848,2586) yields a new equation:
% 220.63/171.13  																																																																																																																																																																												| (1249) all_82_1_108 = 0
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																												| From (848) and (2271) follows:
% 220.63/171.13  																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																												+-Applying beta-rule and splitting (359), into two cases.
% 220.63/171.13  																																																																																																																																																																												|-Branch one:
% 220.63/171.13  																																																																																																																																																																												| (2590)  ~ (aNaturalNumber0(xr) = all_22_2_27)
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																													| From (1931)(1788) and (2590) follows:
% 220.63/171.13  																																																																																																																																																																													| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.63/171.13  																																																																																																																																																																													|
% 220.63/171.13  																																																																																																																																																																													| Using (1665) and (1670) yields:
% 220.63/171.13  																																																																																																																																																																													| (1311) $false
% 220.63/171.13  																																																																																																																																																																													|
% 220.63/171.13  																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																												|-Branch two:
% 220.63/171.13  																																																																																																																																																																												| (2593) aNaturalNumber0(xr) = all_22_2_27
% 220.63/171.13  																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 220.63/171.13  																																																																																																																																																																												|
% 220.63/171.13  																																																																																																																																																																													| From (1931)(1788) and (2593) follows:
% 220.63/171.13  																																																																																																																																																																													| (1665) aNaturalNumber0(xk) = 0
% 220.63/171.13  																																																																																																																																																																													|
% 220.63/171.13  																																																																																																																																																																													+-Applying beta-rule and splitting (924), into two cases.
% 220.63/171.13  																																																																																																																																																																													|-Branch one:
% 220.63/171.13  																																																																																																																																																																													| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 220.63/171.13  																																																																																																																																																																													|
% 220.63/171.13  																																																																																																																																																																														| From (1236) and (2522) follows:
% 220.63/171.13  																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																														| Using (91) and (1934) yields:
% 220.63/171.13  																																																																																																																																																																														| (1311) $false
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																													|-Branch two:
% 220.63/171.13  																																																																																																																																																																													| (2525) aNaturalNumber0(xn) = all_39_7_73
% 220.63/171.13  																																																																																																																																																																													| (2600) all_82_1_108 = all_39_7_73
% 220.63/171.13  																																																																																																																																																																													|
% 220.63/171.13  																																																																																																																																																																														| Combining equations (1249,2600) yields a new equation:
% 220.63/171.13  																																																																																																																																																																														| (1236) all_39_7_73 = 0
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																														| Combining equations (1236,2600) yields a new equation:
% 220.63/171.13  																																																																																																																																																																														| (1249) all_82_1_108 = 0
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																														| From (1236) and (2525) follows:
% 220.63/171.13  																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																														+-Applying beta-rule and splitting (1142), into two cases.
% 220.63/171.13  																																																																																																																																																																														|-Branch one:
% 220.63/171.13  																																																																																																																																																																														| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																															| From (1244) and (2604) follows:
% 220.63/171.13  																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.13  																																																																																																																																																																															|
% 220.63/171.13  																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.63/171.13  																																																																																																																																																																															| (1311) $false
% 220.63/171.13  																																																																																																																																																																															|
% 220.63/171.13  																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.13  																																																																																																																																																																														|-Branch two:
% 220.63/171.13  																																																																																																																																																																														| (2607) aNaturalNumber0(xn) = all_72_1_100
% 220.63/171.13  																																																																																																																																																																														| (2608) all_72_1_100 = all_12_2_12
% 220.63/171.13  																																																																																																																																																																														|
% 220.63/171.13  																																																																																																																																																																															| Combining equations (1244,2608) yields a new equation:
% 220.63/171.13  																																																																																																																																																																															| (1223) all_12_2_12 = 0
% 220.63/171.13  																																																																																																																																																																															|
% 220.63/171.13  																																																																																																																																																																															| Combining equations (1223,2608) yields a new equation:
% 220.63/171.13  																																																																																																																																																																															| (1244) all_72_1_100 = 0
% 220.63/171.13  																																																																																																																																																																															|
% 220.63/171.13  																																																																																																																																																																															| From (1244) and (2607) follows:
% 220.63/171.14  																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.63/171.14  																																																																																																																																																																															|
% 220.63/171.14  																																																																																																																																																																															+-Applying beta-rule and splitting (778), into two cases.
% 220.63/171.14  																																																																																																																																																																															|-Branch one:
% 220.63/171.14  																																																																																																																																																																															| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 220.63/171.14  																																																																																																																																																																															|
% 220.63/171.14  																																																																																																																																																																																| From (1789) and (1945) follows:
% 220.63/171.14  																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																| Using (12) and (1940) yields:
% 220.63/171.14  																																																																																																																																																																																| (1311) $false
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																															|-Branch two:
% 220.63/171.14  																																																																																																																																																																															| (1948) aNaturalNumber0(xm) = all_57_2_90
% 220.63/171.14  																																																																																																																																																																															| (2616) all_57_2_90 = all_37_3_64
% 220.63/171.14  																																																																																																																																																																															|
% 220.63/171.14  																																																																																																																																																																																| Combining equations (1789,2616) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																| (1233) all_37_3_64 = 0
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																| Combining equations (1233,2616) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																| (1789) all_57_2_90 = 0
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																| From (1789) and (1948) follows:
% 220.63/171.14  																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																+-Applying beta-rule and splitting (407), into two cases.
% 220.63/171.14  																																																																																																																																																																																|-Branch one:
% 220.63/171.14  																																																																																																																																																																																| (2620)  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																	| From (1788) and (2620) follows:
% 220.63/171.14  																																																																																																																																																																																	| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																	| Using (1295) and (2129) yields:
% 220.63/171.14  																																																																																																																																																																																	| (1311) $false
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																|-Branch two:
% 220.63/171.14  																																																																																																																																																																																| (2623) aNaturalNumber0(all_0_7_7) = all_22_2_27
% 220.63/171.14  																																																																																																																																																																																| (2624) all_47_2_83 = all_22_2_27
% 220.63/171.14  																																																																																																																																																																																|
% 220.63/171.14  																																																																																																																																																																																	| Combining equations (1293,2624) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																	| (1788) all_22_2_27 = 0
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																	| Combining equations (1788,2624) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																	| From (1788) and (2623) follows:
% 220.63/171.14  																																																																																																																																																																																	| (1295) aNaturalNumber0(all_0_7_7) = 0
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																	+-Applying beta-rule and splitting (836), into two cases.
% 220.63/171.14  																																																																																																																																																																																	|-Branch one:
% 220.63/171.14  																																																																																																																																																																																	| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																		| From (1789) and (1945) follows:
% 220.63/171.14  																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																		| Using (12) and (1940) yields:
% 220.63/171.14  																																																																																																																																																																																		| (1311) $false
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																	|-Branch two:
% 220.63/171.14  																																																																																																																																																																																	| (1948) aNaturalNumber0(xm) = all_57_2_90
% 220.63/171.14  																																																																																																																																																																																	| (2632) all_57_2_90 = all_18_1_20
% 220.63/171.14  																																																																																																																																																																																	|
% 220.63/171.14  																																																																																																																																																																																		| Combining equations (1789,2632) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																		| (1227) all_18_1_20 = 0
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																		| Combining equations (1227,2632) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																		| (1789) all_57_2_90 = 0
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																		| From (1789) and (1948) follows:
% 220.63/171.14  																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																		+-Applying beta-rule and splitting (696), into two cases.
% 220.63/171.14  																																																																																																																																																																																		|-Branch one:
% 220.63/171.14  																																																																																																																																																																																		| (2636)  ~ (aNaturalNumber0(sz10) = all_72_1_100)
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																			| From (1244) and (2636) follows:
% 220.63/171.14  																																																																																																																																																																																			| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.63/171.14  																																																																																																																																																																																			|
% 220.63/171.14  																																																																																																																																																																																			| Using (61) and (1994) yields:
% 220.63/171.14  																																																																																																																																																																																			| (1311) $false
% 220.63/171.14  																																																																																																																																																																																			|
% 220.63/171.14  																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																		|-Branch two:
% 220.63/171.14  																																																																																																																																																																																		| (2639) aNaturalNumber0(sz10) = all_72_1_100
% 220.63/171.14  																																																																																																																																																																																		| (1244) all_72_1_100 = 0
% 220.63/171.14  																																																																																																																																																																																		|
% 220.63/171.14  																																																																																																																																																																																			| From (1244) and (2639) follows:
% 220.63/171.14  																																																																																																																																																																																			| (61) aNaturalNumber0(sz10) = 0
% 220.63/171.14  																																																																																																																																																																																			|
% 220.63/171.14  																																																																																																																																																																																			+-Applying beta-rule and splitting (682), into two cases.
% 220.63/171.14  																																																																																																																																																																																			|-Branch one:
% 220.63/171.14  																																																																																																																																																																																			| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 220.63/171.14  																																																																																																																																																																																			|
% 220.63/171.14  																																																																																																																																																																																				| From (1791) and (2642) follows:
% 220.63/171.14  																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																				| Using (9) and (2008) yields:
% 220.63/171.14  																																																																																																																																																																																				| (1311) $false
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																			|-Branch two:
% 220.63/171.14  																																																																																																																																																																																			| (2645) aNaturalNumber0(xp) = all_72_2_101
% 220.63/171.14  																																																																																																																																																																																			| (2646) all_72_2_101 = all_24_1_29
% 220.63/171.14  																																																																																																																																																																																			|
% 220.63/171.14  																																																																																																																																																																																				| Combining equations (1791,2646) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																				| (1207) all_24_1_29 = 0
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																				| Combining equations (1207,2646) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																				| (1791) all_72_2_101 = 0
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																				| From (1791) and (2645) follows:
% 220.63/171.14  																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																				+-Applying beta-rule and splitting (648), into two cases.
% 220.63/171.14  																																																																																																																																																																																				|-Branch one:
% 220.63/171.14  																																																																																																																																																																																				| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																					| From (1791) and (2642) follows:
% 220.63/171.14  																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																					| Using (9) and (2008) yields:
% 220.63/171.14  																																																																																																																																																																																					| (1311) $false
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																				|-Branch two:
% 220.63/171.14  																																																																																																																																																																																				| (2645) aNaturalNumber0(xp) = all_72_2_101
% 220.63/171.14  																																																																																																																																																																																				| (2654) all_72_2_101 = all_37_2_63
% 220.63/171.14  																																																																																																																																																																																				|
% 220.63/171.14  																																																																																																																																																																																					| Combining equations (1791,2654) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																					| (1195) all_37_2_63 = 0
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																					| Combining equations (1195,2654) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																					| (1791) all_72_2_101 = 0
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																					| From (1791) and (2645) follows:
% 220.63/171.14  																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																					+-Applying beta-rule and splitting (570), into two cases.
% 220.63/171.14  																																																																																																																																																																																					|-Branch one:
% 220.63/171.14  																																																																																																																																																																																					| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																						| From (1790) and (2506) follows:
% 220.63/171.14  																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.14  																																																																																																																																																																																						|
% 220.63/171.14  																																																																																																																																																																																						| Using (9) and (2008) yields:
% 220.63/171.14  																																																																																																																																																																																						| (1311) $false
% 220.63/171.14  																																																																																																																																																																																						|
% 220.63/171.14  																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																					|-Branch two:
% 220.63/171.14  																																																																																																																																																																																					| (2509) aNaturalNumber0(xp) = all_62_2_94
% 220.63/171.14  																																																																																																																																																																																					| (2662) all_67_3_98 = all_62_2_94
% 220.63/171.14  																																																																																																																																																																																					|
% 220.63/171.14  																																																																																																																																																																																						| Combining equations (1241,2662) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																						| (1790) all_62_2_94 = 0
% 220.63/171.14  																																																																																																																																																																																						|
% 220.63/171.14  																																																																																																																																																																																						| From (1790) and (2509) follows:
% 220.63/171.14  																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 220.63/171.14  																																																																																																																																																																																						|
% 220.63/171.14  																																																																																																																																																																																						+-Applying beta-rule and splitting (583), into two cases.
% 220.63/171.14  																																																																																																																																																																																						|-Branch one:
% 220.63/171.14  																																																																																																																																																																																						| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 220.63/171.14  																																																																																																																																																																																						|
% 220.63/171.14  																																																																																																																																																																																							| From (1829) and (2665) follows:
% 220.63/171.14  																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.14  																																																																																																																																																																																							|
% 220.63/171.14  																																																																																																																																																																																							| Using (9) and (2008) yields:
% 220.63/171.14  																																																																																																																																																																																							| (1311) $false
% 220.63/171.14  																																																																																																																																																																																							|
% 220.63/171.14  																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																						|-Branch two:
% 220.63/171.14  																																																																																																																																																																																						| (2668) aNaturalNumber0(xp) = all_67_2_97
% 220.63/171.14  																																																																																																																																																																																						| (2669) all_67_2_97 = all_57_3_91
% 220.63/171.14  																																																																																																																																																																																						|
% 220.63/171.14  																																																																																																																																																																																							| Combining equations (1829,2669) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																							| (2199) all_57_3_91 = 0
% 220.63/171.14  																																																																																																																																																																																							|
% 220.63/171.14  																																																																																																																																																																																							| Combining equations (2199,2669) yields a new equation:
% 220.63/171.14  																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 220.63/171.14  																																																																																																																																																																																							|
% 220.63/171.14  																																																																																																																																																																																							| From (1829) and (2668) follows:
% 220.63/171.14  																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 220.63/171.14  																																																																																																																																																																																							|
% 220.63/171.14  																																																																																																																																																																																							+-Applying beta-rule and splitting (567), into two cases.
% 220.63/171.14  																																																																																																																																																																																							|-Branch one:
% 220.63/171.14  																																																																																																																																																																																							| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 220.63/171.14  																																																																																																																																																																																							|
% 220.63/171.14  																																																																																																																																																																																								| From (1829) and (2665) follows:
% 220.63/171.14  																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.14  																																																																																																																																																																																								|
% 220.63/171.14  																																																																																																																																																																																								| Using (9) and (2008) yields:
% 220.63/171.14  																																																																																																																																																																																								| (1311) $false
% 220.63/171.14  																																																																																																																																																																																								|
% 220.63/171.14  																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.63/171.14  																																																																																																																																																																																							|-Branch two:
% 220.63/171.14  																																																																																																																																																																																							| (2668) aNaturalNumber0(xp) = all_67_2_97
% 220.63/171.14  																																																																																																																																																																																							| (2677) all_67_2_97 = all_67_3_98
% 220.63/171.15  																																																																																																																																																																																							|
% 220.63/171.15  																																																																																																																																																																																								| Combining equations (1829,2677) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																								| (1241) all_67_3_98 = 0
% 220.63/171.15  																																																																																																																																																																																								|
% 220.63/171.15  																																																																																																																																																																																								| Combining equations (1241,2677) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 220.63/171.15  																																																																																																																																																																																								|
% 220.63/171.15  																																																																																																																																																																																								| From (1829) and (2668) follows:
% 220.63/171.15  																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 220.63/171.15  																																																																																																																																																																																								|
% 220.63/171.15  																																																																																																																																																																																								+-Applying beta-rule and splitting (1064), into two cases.
% 220.63/171.15  																																																																																																																																																																																								|-Branch one:
% 220.63/171.15  																																																																																																																																																																																								| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.63/171.15  																																																																																																																																																																																								|
% 220.63/171.15  																																																																																																																																																																																									| From (1282) and (2210) follows:
% 220.63/171.15  																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																									| Using (91) and (1934) yields:
% 220.63/171.15  																																																																																																																																																																																									| (1311) $false
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																								|-Branch two:
% 220.63/171.15  																																																																																																																																																																																								| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.63/171.15  																																																																																																																																																																																								| (2685) all_24_2_30 = all_18_2_21
% 220.63/171.15  																																																																																																																																																																																								|
% 220.63/171.15  																																																																																																																																																																																									| Combining equations (1282,2685) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																									| (1226) all_18_2_21 = 0
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																									| Combining equations (1226,2685) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																									| From (1282) and (2213) follows:
% 220.63/171.15  																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																									+-Applying beta-rule and splitting (617), into two cases.
% 220.63/171.15  																																																																																																																																																																																									|-Branch one:
% 220.63/171.15  																																																																																																																																																																																									| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																										| From (1790) and (2506) follows:
% 220.63/171.15  																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																										| Using (9) and (2008) yields:
% 220.63/171.15  																																																																																																																																																																																										| (1311) $false
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																									|-Branch two:
% 220.63/171.15  																																																																																																																																																																																									| (2509) aNaturalNumber0(xp) = all_62_2_94
% 220.63/171.15  																																																																																																																																																																																									| (2693) all_62_2_94 = all_47_3_84
% 220.63/171.15  																																																																																																																																																																																									|
% 220.63/171.15  																																																																																																																																																																																										| Combining equations (2693,1790) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																										| (2694) all_47_3_84 = 0
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																										| Simplifying 2694 yields:
% 220.63/171.15  																																																																																																																																																																																										| (2191) all_47_3_84 = 0
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																										| From (1790) and (2509) follows:
% 220.63/171.15  																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																										+-Applying beta-rule and splitting (588), into two cases.
% 220.63/171.15  																																																																																																																																																																																										|-Branch one:
% 220.63/171.15  																																																																																																																																																																																										| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																											| From (1788) and (2105) follows:
% 220.63/171.15  																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																											| Using (9) and (2008) yields:
% 220.63/171.15  																																																																																																																																																																																											| (1311) $false
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																										|-Branch two:
% 220.63/171.15  																																																																																																																																																																																										| (2108) aNaturalNumber0(xp) = all_22_2_27
% 220.63/171.15  																																																																																																																																																																																										| (2701) all_57_3_91 = all_22_2_27
% 220.63/171.15  																																																																																																																																																																																										|
% 220.63/171.15  																																																																																																																																																																																											| Combining equations (2199,2701) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																											| Combining equations (1788,2701) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																											| (2199) all_57_3_91 = 0
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																											| From (1788) and (2108) follows:
% 220.63/171.15  																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																											+-Applying beta-rule and splitting (837), into two cases.
% 220.63/171.15  																																																																																																																																																																																											|-Branch one:
% 220.63/171.15  																																																																																																																																																																																											| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																												| From (1788) and (2144) follows:
% 220.63/171.15  																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.15  																																																																																																																																																																																												|
% 220.63/171.15  																																																																																																																																																																																												| Using (12) and (1940) yields:
% 220.63/171.15  																																																																																																																																																																																												| (1311) $false
% 220.63/171.15  																																																																																																																																																																																												|
% 220.63/171.15  																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																											|-Branch two:
% 220.63/171.15  																																																																																																																																																																																											| (2147) aNaturalNumber0(xm) = all_22_2_27
% 220.63/171.15  																																																																																																																																																																																											| (2709) all_22_2_27 = all_18_1_20
% 220.63/171.15  																																																																																																																																																																																											|
% 220.63/171.15  																																																																																																																																																																																												| From (1788) and (2147) follows:
% 220.63/171.15  																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 220.63/171.15  																																																																																																																																																																																												|
% 220.63/171.15  																																																																																																																																																																																												+-Applying beta-rule and splitting (839), into two cases.
% 220.63/171.15  																																																																																																																																																																																												|-Branch one:
% 220.63/171.15  																																																																																																																																																																																												| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 220.63/171.15  																																																																																																																																																																																												|
% 220.63/171.15  																																																																																																																																																																																													| From (1294) and (2275) follows:
% 220.63/171.15  																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																													| Using (12) and (1940) yields:
% 220.63/171.15  																																																																																																																																																																																													| (1311) $false
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																												|-Branch two:
% 220.63/171.15  																																																																																																																																																																																												| (2278) aNaturalNumber0(xm) = all_77_2_105
% 220.63/171.15  																																																																																																																																																																																												| (2715) all_77_2_105 = all_18_1_20
% 220.63/171.15  																																																																																																																																																																																												|
% 220.63/171.15  																																																																																																																																																																																													| Combining equations (1294,2715) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																													| (1227) all_18_1_20 = 0
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																													| Combining equations (1227,2715) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																													| From (1294) and (2278) follows:
% 220.63/171.15  																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																													+-Applying beta-rule and splitting (348), into two cases.
% 220.63/171.15  																																																																																																																																																																																													|-Branch one:
% 220.63/171.15  																																																																																																																																																																																													| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																														| From (1828) and (2498) follows:
% 220.63/171.15  																																																																																																																																																																																														| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																														| Using (1775) and (1780) yields:
% 220.63/171.15  																																																																																																																																																																																														| (1311) $false
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																													|-Branch two:
% 220.63/171.15  																																																																																																																																																																																													| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 220.63/171.15  																																																																																																																																																																																													| (2723) all_62_2_94 = all_20_0_22
% 220.63/171.15  																																																																																																																																																																																													|
% 220.63/171.15  																																																																																																																																																																																														| Combining equations (2723,1790) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																														| (2724) all_20_0_22 = 0
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																														| Simplifying 2724 yields:
% 220.63/171.15  																																																																																																																																																																																														| (1828) all_20_0_22 = 0
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																														| From (1828) and (2501) follows:
% 220.63/171.15  																																																																																																																																																																																														| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																														+-Applying beta-rule and splitting (979), into two cases.
% 220.63/171.15  																																																																																																																																																																																														|-Branch one:
% 220.63/171.15  																																																																																																																																																																																														| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																															| From (1221) and (2081) follows:
% 220.63/171.15  																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.63/171.15  																																																																																																																																																																																															| (1311) $false
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																														|-Branch two:
% 220.63/171.15  																																																																																																																																																																																														| (2084) aNaturalNumber0(xn) = all_12_1_11
% 220.63/171.15  																																																																																																																																																																																														| (2731) all_62_1_93 = all_12_1_11
% 220.63/171.15  																																																																																																																																																																																														|
% 220.63/171.15  																																																																																																																																																																																															| Combining equations (1240,2731) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																															| (1221) all_12_1_11 = 0
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																															| Combining equations (1221,2731) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																															| (1240) all_62_1_93 = 0
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																															| From (1221) and (2084) follows:
% 220.63/171.15  																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																															+-Applying beta-rule and splitting (431), into two cases.
% 220.63/171.15  																																																																																																																																																																																															|-Branch one:
% 220.63/171.15  																																																																																																																																																																																															| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																																| Using (1351) and (2575) yields:
% 220.63/171.15  																																																																																																																																																																																																| (1311) $false
% 220.63/171.15  																																																																																																																																																																																																|
% 220.63/171.15  																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																															|-Branch two:
% 220.63/171.15  																																																																																																																																																																																															| (1351) aNaturalNumber0(all_0_8_8) = 0
% 220.63/171.15  																																																																																																																																																																																															| (1350) all_24_0_28 = 0
% 220.63/171.15  																																																																																																																																																																																															|
% 220.63/171.15  																																																																																																																																																																																																+-Applying beta-rule and splitting (1038), into two cases.
% 220.63/171.15  																																																																																																																																																																																																|-Branch one:
% 220.63/171.15  																																																																																																																																																																																																| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 220.63/171.15  																																																																																																																																																																																																|
% 220.63/171.15  																																																																																																																																																																																																	| From (1350) and (1985) follows:
% 220.63/171.15  																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.15  																																																																																																																																																																																																	|
% 220.63/171.15  																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 220.63/171.15  																																																																																																																																																																																																	| (1311) $false
% 220.63/171.15  																																																																																																																																																																																																	|
% 220.63/171.15  																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																																|-Branch two:
% 220.63/171.15  																																																																																																																																																																																																| (1988) aNaturalNumber0(xn) = all_24_0_28
% 220.63/171.15  																																																																																																																																																																																																| (2743) all_37_4_65 = all_24_0_28
% 220.63/171.15  																																																																																																																																																																																																|
% 220.63/171.15  																																																																																																																																																																																																	| Combining equations (1232,2743) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																																	| (1350) all_24_0_28 = 0
% 220.63/171.15  																																																																																																																																																																																																	|
% 220.63/171.15  																																																																																																																																																																																																	| Combining equations (1350,2743) yields a new equation:
% 220.63/171.15  																																																																																																																																																																																																	| (1232) all_37_4_65 = 0
% 220.63/171.15  																																																																																																																																																																																																	|
% 220.63/171.15  																																																																																																																																																																																																	| From (1350) and (1988) follows:
% 220.63/171.15  																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 220.63/171.15  																																																																																																																																																																																																	|
% 220.63/171.15  																																																																																																																																																																																																	+-Applying beta-rule and splitting (943), into two cases.
% 220.63/171.15  																																																																																																																																																																																																	|-Branch one:
% 220.63/171.15  																																																																																																																																																																																																	| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 220.63/171.15  																																																																																																																																																																																																	|
% 220.63/171.15  																																																																																																																																																																																																		| From (1281) and (2374) follows:
% 220.63/171.15  																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.15  																																																																																																																																																																																																		|
% 220.63/171.15  																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 220.63/171.15  																																																																																																																																																																																																		| (1311) $false
% 220.63/171.15  																																																																																																																																																																																																		|
% 220.63/171.15  																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.63/171.15  																																																																																																																																																																																																	|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																	| (2377) aNaturalNumber0(xn) = all_12_0_10
% 220.63/171.16  																																																																																																																																																																																																	| (2751) all_77_1_104 = all_12_0_10
% 220.63/171.16  																																																																																																																																																																																																	|
% 220.63/171.16  																																																																																																																																																																																																		| Combining equations (1246,2751) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 220.63/171.16  																																																																																																																																																																																																		|
% 220.63/171.16  																																																																																																																																																																																																		| Combining equations (1281,2751) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																		| (1246) all_77_1_104 = 0
% 220.63/171.16  																																																																																																																																																																																																		|
% 220.63/171.16  																																																																																																																																																																																																		| From (1281) and (2377) follows:
% 220.63/171.16  																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 220.63/171.16  																																																																																																																																																																																																		|
% 220.63/171.16  																																																																																																																																																																																																		+-Applying beta-rule and splitting (420), into two cases.
% 220.63/171.16  																																																																																																																																																																																																		|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																		| (2755)  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 220.63/171.16  																																																																																																																																																																																																		|
% 220.63/171.16  																																																																																																																																																																																																			| From (1790) and (2755) follows:
% 220.63/171.16  																																																																																																																																																																																																			| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																			| Using (1295) and (2129) yields:
% 220.63/171.16  																																																																																																																																																																																																			| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																		|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																		| (2758) aNaturalNumber0(all_0_7_7) = all_62_2_94
% 220.63/171.16  																																																																																																																																																																																																		| (2759) all_62_2_94 = all_16_0_16
% 220.63/171.16  																																																																																																																																																																																																		|
% 220.63/171.16  																																																																																																																																																																																																			| Combining equations (2759,1790) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																			| (2760) all_16_0_16 = 0
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																			| Simplifying 2760 yields:
% 220.63/171.16  																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																			| From (1790) and (2758) follows:
% 220.63/171.16  																																																																																																																																																																																																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																			+-Applying beta-rule and splitting (341), into two cases.
% 220.63/171.16  																																																																																																																																																																																																			|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																			| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																				| From (1790) and (2506) follows:
% 220.63/171.16  																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.16  																																																																																																																																																																																																				|
% 220.63/171.16  																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 220.63/171.16  																																																																																																																																																																																																				| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																				|
% 220.63/171.16  																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																			|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																			| (2509) aNaturalNumber0(xp) = all_62_2_94
% 220.63/171.16  																																																																																																																																																																																																			| (1790) all_62_2_94 = 0
% 220.63/171.16  																																																																																																																																																																																																			|
% 220.63/171.16  																																																																																																																																																																																																				| From (1790) and (2509) follows:
% 220.63/171.16  																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 220.63/171.16  																																																																																																																																																																																																				|
% 220.63/171.16  																																																																																																																																																																																																				+-Applying beta-rule and splitting (669), into two cases.
% 220.63/171.16  																																																																																																																																																																																																				|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																				| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 220.63/171.16  																																																																																																																																																																																																				|
% 220.63/171.16  																																																																																																																																																																																																					| From (1788) and (2105) follows:
% 220.63/171.16  																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 220.63/171.16  																																																																																																																																																																																																					| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																				|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																				| (2108) aNaturalNumber0(xp) = all_22_2_27
% 220.63/171.16  																																																																																																																																																																																																				| (2773) all_26_1_32 = all_22_2_27
% 220.63/171.16  																																																																																																																																																																																																				|
% 220.63/171.16  																																																																																																																																																																																																					| Combining equations (1202,2773) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																					| (1788) all_22_2_27 = 0
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																					| Combining equations (1788,2773) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																					| (1202) all_26_1_32 = 0
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																					| From (1788) and (2108) follows:
% 220.63/171.16  																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																					+-Applying beta-rule and splitting (923), into two cases.
% 220.63/171.16  																																																																																																																																																																																																					|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																					| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																						| From (1237) and (2490) follows:
% 220.63/171.16  																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 220.63/171.16  																																																																																																																																																																																																						| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																					|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																					| (2493) aNaturalNumber0(xn) = all_47_1_82
% 220.63/171.16  																																																																																																																																																																																																					| (2781) all_82_1_108 = all_47_1_82
% 220.63/171.16  																																																																																																																																																																																																					|
% 220.63/171.16  																																																																																																																																																																																																						| Combining equations (1249,2781) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																						| (1237) all_47_1_82 = 0
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																						| Combining equations (1237,2781) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																						| (1249) all_82_1_108 = 0
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																						| From (1237) and (2493) follows:
% 220.63/171.16  																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																						+-Applying beta-rule and splitting (720), into two cases.
% 220.63/171.16  																																																																																																																																																																																																						|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																						| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																							| From (1790) and (1939) follows:
% 220.63/171.16  																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 220.63/171.16  																																																																																																																																																																																																							| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																						|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																						| (1942) aNaturalNumber0(xm) = all_62_2_94
% 220.63/171.16  																																																																																																																																																																																																						| (2789) all_67_1_96 = all_62_2_94
% 220.63/171.16  																																																																																																																																																																																																						|
% 220.63/171.16  																																																																																																																																																																																																							| Combining equations (1242,2789) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																							| (1790) all_62_2_94 = 0
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																							| Combining equations (1790,2789) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																							| (1242) all_67_1_96 = 0
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																							| From (1790) and (1942) follows:
% 220.63/171.16  																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																							+-Applying beta-rule and splitting (602), into two cases.
% 220.63/171.16  																																																																																																																																																																																																							|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																							| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																								| From (1789) and (2186) follows:
% 220.63/171.16  																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 220.63/171.16  																																																																																																																																																																																																								| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																							|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																							| (2189) aNaturalNumber0(xp) = all_57_2_90
% 220.63/171.16  																																																																																																																																																																																																							| (2797) all_57_2_90 = all_52_1_86
% 220.63/171.16  																																																																																																																																																																																																							|
% 220.63/171.16  																																																																																																																																																																																																								| Combining equations (1789,2797) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																								| (1238) all_52_1_86 = 0
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																								| Combining equations (1238,2797) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																								| (1789) all_57_2_90 = 0
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																								| From (1789) and (2189) follows:
% 220.63/171.16  																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																								+-Applying beta-rule and splitting (504), into two cases.
% 220.63/171.16  																																																																																																																																																																																																								|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																								| (2801)  ~ (aNaturalNumber0(xk) = all_82_2_109)
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																									| From (1830) and (2801) follows:
% 220.63/171.16  																																																																																																																																																																																																									| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.63/171.16  																																																																																																																																																																																																									|
% 220.63/171.16  																																																																																																																																																																																																									| Using (1665) and (1670) yields:
% 220.63/171.16  																																																																																																																																																																																																									| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																									|
% 220.63/171.16  																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																								|-Branch two:
% 220.63/171.16  																																																																																																																																																																																																								| (2804) aNaturalNumber0(xk) = all_82_2_109
% 220.63/171.16  																																																																																																																																																																																																								| (2805) all_82_2_109 = all_52_2_87
% 220.63/171.16  																																																																																																																																																																																																								|
% 220.63/171.16  																																																																																																																																																																																																									| Combining equations (1830,2805) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																									| (1674) all_52_2_87 = 0
% 220.63/171.16  																																																																																																																																																																																																									|
% 220.63/171.16  																																																																																																																																																																																																									| Combining equations (1674,2805) yields a new equation:
% 220.63/171.16  																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 220.63/171.16  																																																																																																																																																																																																									|
% 220.63/171.16  																																																																																																																																																																																																									| From (1830) and (2804) follows:
% 220.63/171.16  																																																																																																																																																																																																									| (1665) aNaturalNumber0(xk) = 0
% 220.63/171.16  																																																																																																																																																																																																									|
% 220.63/171.16  																																																																																																																																																																																																									+-Applying beta-rule and splitting (441), into two cases.
% 220.63/171.16  																																																																																																																																																																																																									|-Branch one:
% 220.63/171.16  																																																																																																																																																																																																									| (2809)  ~ (aNaturalNumber0(all_0_8_8) = all_47_2_83)
% 220.63/171.16  																																																																																																																																																																																																									|
% 220.63/171.16  																																																																																																																																																																																																										| From (1293) and (2809) follows:
% 220.63/171.16  																																																																																																																																																																																																										| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 220.63/171.16  																																																																																																																																																																																																										|
% 220.63/171.16  																																																																																																																																																																																																										| Using (1351) and (2575) yields:
% 220.63/171.16  																																																																																																																																																																																																										| (1311) $false
% 220.63/171.16  																																																																																																																																																																																																										|
% 220.63/171.16  																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.63/171.16  																																																																																																																																																																																																									|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																									| (2812) aNaturalNumber0(all_0_8_8) = all_47_2_83
% 220.63/171.17  																																																																																																																																																																																																									| (2813) all_47_2_83 = all_24_0_28
% 220.63/171.17  																																																																																																																																																																																																									|
% 220.63/171.17  																																																																																																																																																																																																										| Combining equations (1293,2813) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																										| (1350) all_24_0_28 = 0
% 220.63/171.17  																																																																																																																																																																																																										|
% 220.63/171.17  																																																																																																																																																																																																										| Combining equations (1350,2813) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																										| (1293) all_47_2_83 = 0
% 220.63/171.17  																																																																																																																																																																																																										|
% 220.63/171.17  																																																																																																																																																																																																										| From (1293) and (2812) follows:
% 220.63/171.17  																																																																																																																																																																																																										| (1351) aNaturalNumber0(all_0_8_8) = 0
% 220.63/171.17  																																																																																																																																																																																																										|
% 220.63/171.17  																																																																																																																																																																																																										+-Applying beta-rule and splitting (765), into two cases.
% 220.63/171.17  																																																																																																																																																																																																										|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																										| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 220.63/171.17  																																																																																																																																																																																																										|
% 220.63/171.17  																																																																																																																																																																																																											| From (1350) and (2136) follows:
% 220.63/171.17  																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 220.63/171.17  																																																																																																																																																																																																											| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																										|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																										| (2139) aNaturalNumber0(xm) = all_24_0_28
% 220.63/171.17  																																																																																																																																																																																																										| (2821) all_39_7_73 = all_24_0_28
% 220.63/171.17  																																																																																																																																																																																																										|
% 220.63/171.17  																																																																																																																																																																																																											| Combining equations (1236,2821) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																											| Combining equations (1350,2821) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																											| (1236) all_39_7_73 = 0
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																											| From (1350) and (2139) follows:
% 220.63/171.17  																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																											+-Applying beta-rule and splitting (800), into two cases.
% 220.63/171.17  																																																																																																																																																																																																											|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																											| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																												| From (1789) and (1945) follows:
% 220.63/171.17  																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 220.63/171.17  																																																																																																																																																																																																												| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																											|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																											| (1948) aNaturalNumber0(xm) = all_57_2_90
% 220.63/171.17  																																																																																																																																																																																																											| (2829) all_57_2_90 = all_22_1_26
% 220.63/171.17  																																																																																																																																																																																																											|
% 220.63/171.17  																																																																																																																																																																																																												| Combining equations (1789,2829) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																												| (1229) all_22_1_26 = 0
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																												| Combining equations (1229,2829) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																												| From (1789) and (1948) follows:
% 220.63/171.17  																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																												+-Applying beta-rule and splitting (651), into two cases.
% 220.63/171.17  																																																																																																																																																																																																												|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																												| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																													| From (1788) and (2105) follows:
% 220.63/171.17  																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 220.63/171.17  																																																																																																																																																																																																													| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																												|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																												| (2108) aNaturalNumber0(xp) = all_22_2_27
% 220.63/171.17  																																																																																																																																																																																																												| (2837) all_37_2_63 = all_22_2_27
% 220.63/171.17  																																																																																																																																																																																																												|
% 220.63/171.17  																																																																																																																																																																																																													| Combining equations (1195,2837) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																													| (1788) all_22_2_27 = 0
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																													| Combining equations (1788,2837) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																													| (1195) all_37_2_63 = 0
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																													| From (1788) and (2108) follows:
% 220.63/171.17  																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																													+-Applying beta-rule and splitting (950), into two cases.
% 220.63/171.17  																																																																																																																																																																																																													|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																													| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																														| From (1228) and (2055) follows:
% 220.63/171.17  																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 220.63/171.17  																																																																																																																																																																																																														| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																													|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																													| (2058) aNaturalNumber0(xn) = all_20_1_23
% 220.63/171.17  																																																																																																																																																																																																													| (2845) all_77_1_104 = all_20_1_23
% 220.63/171.17  																																																																																																																																																																																																													|
% 220.63/171.17  																																																																																																																																																																																																														| Combining equations (1246,2845) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																														| (1228) all_20_1_23 = 0
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																														| Combining equations (1228,2845) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																														| (1246) all_77_1_104 = 0
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																														| From (1228) and (2058) follows:
% 220.63/171.17  																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																														+-Applying beta-rule and splitting (1100), into two cases.
% 220.63/171.17  																																																																																																																																																																																																														|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																														| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																															| From (848) and (2268) follows:
% 220.63/171.17  																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.17  																																																																																																																																																																																																															|
% 220.63/171.17  																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.63/171.17  																																																																																																																																																																																																															| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																															|
% 220.63/171.17  																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																														|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																														| (2271) aNaturalNumber0(xn) = all_16_1_17
% 220.63/171.17  																																																																																																																																																																																																														| (2853) all_16_1_17 = all_16_2_18
% 220.63/171.17  																																																																																																																																																																																																														|
% 220.63/171.17  																																																																																																																																																																																																															| From (848) and (2271) follows:
% 220.63/171.17  																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.63/171.17  																																																																																																																																																																																																															|
% 220.63/171.17  																																																																																																																																																																																																															+-Applying beta-rule and splitting (362), into two cases.
% 220.63/171.17  																																																																																																																																																																																																															|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																															| (2855)  ~ (aNaturalNumber0(sz10) = all_22_2_27)
% 220.63/171.17  																																																																																																																																																																																																															|
% 220.63/171.17  																																																																																																																																																																																																																| From (1788) and (2855) follows:
% 220.63/171.17  																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.63/171.17  																																																																																																																																																																																																																|
% 220.63/171.17  																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 220.63/171.17  																																																																																																																																																																																																																| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																																|
% 220.63/171.17  																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																															|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																															| (2858) aNaturalNumber0(sz10) = all_22_2_27
% 220.63/171.17  																																																																																																																																																																																																															| (1788) all_22_2_27 = 0
% 220.63/171.17  																																																																																																																																																																																																															|
% 220.63/171.17  																																																																																																																																																																																																																| From (1788) and (2858) follows:
% 220.63/171.17  																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 220.63/171.17  																																																																																																																																																																																																																|
% 220.63/171.17  																																																																																																																																																																																																																+-Applying beta-rule and splitting (659), into two cases.
% 220.63/171.17  																																																																																																																																																																																																																|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																																| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 220.63/171.17  																																																																																																																																																																																																																|
% 220.63/171.17  																																																																																																																																																																																																																	| From (1281) and (2039) follows:
% 220.63/171.17  																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.17  																																																																																																																																																																																																																	|
% 220.63/171.17  																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 220.63/171.17  																																																																																																																																																																																																																	| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																																	|
% 220.63/171.17  																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																																|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																																| (2042) aNaturalNumber0(xp) = all_12_0_10
% 220.63/171.17  																																																																																																																																																																																																																| (2865) all_37_2_63 = all_12_0_10
% 220.63/171.17  																																																																																																																																																																																																																|
% 220.63/171.17  																																																																																																																																																																																																																	| Combining equations (1195,2865) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 220.63/171.17  																																																																																																																																																																																																																	|
% 220.63/171.17  																																																																																																																																																																																																																	| From (1281) and (2042) follows:
% 220.63/171.17  																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 220.63/171.17  																																																																																																																																																																																																																	|
% 220.63/171.17  																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1087), into two cases.
% 220.63/171.17  																																																																																																																																																																																																																	|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																																	| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 220.63/171.17  																																																																																																																																																																																																																	|
% 220.63/171.17  																																																																																																																																																																																																																		| From (1350) and (1985) follows:
% 220.63/171.17  																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 220.63/171.17  																																																																																																																																																																																																																		| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																																	|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																																	| (1988) aNaturalNumber0(xn) = all_24_0_28
% 220.63/171.17  																																																																																																																																																																																																																	| (2872) all_24_0_28 = all_16_2_18
% 220.63/171.17  																																																																																																																																																																																																																	|
% 220.63/171.17  																																																																																																																																																																																																																		| Combining equations (1350,2872) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																																		| (1225) all_16_2_18 = 0
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																		| Combining equations (1225,2872) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																		| From (1350) and (1988) follows:
% 220.63/171.17  																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																		+-Applying beta-rule and splitting (673), into two cases.
% 220.63/171.17  																																																																																																																																																																																																																		|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																																		| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																			| From (1292) and (2023) follows:
% 220.63/171.17  																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.17  																																																																																																																																																																																																																			|
% 220.63/171.17  																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 220.63/171.17  																																																																																																																																																																																																																			| (1311) $false
% 220.63/171.17  																																																																																																																																																																																																																			|
% 220.63/171.17  																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.63/171.17  																																																																																																																																																																																																																		|-Branch two:
% 220.63/171.17  																																																																																																																																																																																																																		| (2026) aNaturalNumber0(xp) = all_16_0_16
% 220.63/171.17  																																																																																																																																																																																																																		| (2880) all_26_1_32 = all_16_0_16
% 220.63/171.17  																																																																																																																																																																																																																		|
% 220.63/171.17  																																																																																																																																																																																																																			| Combining equations (1202,2880) yields a new equation:
% 220.63/171.17  																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 220.63/171.17  																																																																																																																																																																																																																			|
% 220.63/171.17  																																																																																																																																																																																																																			| From (1292) and (2026) follows:
% 220.63/171.17  																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 220.63/171.17  																																																																																																																																																																																																																			|
% 220.63/171.17  																																																																																																																																																																																																																			+-Applying beta-rule and splitting (423), into two cases.
% 220.63/171.17  																																																																																																																																																																																																																			|-Branch one:
% 220.63/171.17  																																																																																																																																																																																																																			| (2883)  ~ (aNaturalNumber0(all_0_7_7) = all_20_2_24)
% 220.63/171.17  																																																																																																																																																																																																																			|
% 220.63/171.17  																																																																																																																																																																																																																				| From (1787) and (2883) follows:
% 220.63/171.18  																																																																																																																																																																																																																				| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																				| Using (1295) and (2129) yields:
% 220.63/171.18  																																																																																																																																																																																																																				| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																			|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																			| (2886) aNaturalNumber0(all_0_7_7) = all_20_2_24
% 220.63/171.18  																																																																																																																																																																																																																			| (2887) all_20_2_24 = all_16_0_16
% 220.63/171.18  																																																																																																																																																																																																																			|
% 220.63/171.18  																																																																																																																																																																																																																				| Combining equations (1787,2887) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																				| Combining equations (1292,2887) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																				| (1787) all_20_2_24 = 0
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																				| From (1787) and (2886) follows:
% 220.63/171.18  																																																																																																																																																																																																																				| (1295) aNaturalNumber0(all_0_7_7) = 0
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1097), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																				|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																				| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																					| From (1229) and (2891) follows:
% 220.63/171.18  																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 220.63/171.18  																																																																																																																																																																																																																					| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																				|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																				| (2894) aNaturalNumber0(xn) = all_22_1_26
% 220.63/171.18  																																																																																																																																																																																																																				| (2895) all_22_1_26 = all_16_2_18
% 220.63/171.18  																																																																																																																																																																																																																				|
% 220.63/171.18  																																																																																																																																																																																																																					| Combining equations (1229,2895) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																					| (1225) all_16_2_18 = 0
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																					| Combining equations (1225,2895) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																					| (1229) all_22_1_26 = 0
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																					| From (1229) and (2894) follows:
% 220.63/171.18  																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																					+-Applying beta-rule and splitting (641), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																					|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																					| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																						| From (1350) and (2899) follows:
% 220.63/171.18  																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.18  																																																																																																																																																																																																																						|
% 220.63/171.18  																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 220.63/171.18  																																																																																																																																																																																																																						| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																						|
% 220.63/171.18  																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																					|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																					| (2902) aNaturalNumber0(xp) = all_24_0_28
% 220.63/171.18  																																																																																																																																																																																																																					| (2903) all_39_6_72 = all_24_0_28
% 220.63/171.18  																																																																																																																																																																																																																					|
% 220.63/171.18  																																																																																																																																																																																																																						| Combining equations (629,2903) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																						| (1350) all_24_0_28 = 0
% 220.63/171.18  																																																																																																																																																																																																																						|
% 220.63/171.18  																																																																																																																																																																																																																						| From (1350) and (2902) follows:
% 220.63/171.18  																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 220.63/171.18  																																																																																																																																																																																																																						|
% 220.63/171.18  																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1092), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																						|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																						| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 220.63/171.18  																																																																																																																																																																																																																						|
% 220.63/171.18  																																																																																																																																																																																																																							| From (1244) and (2604) follows:
% 220.63/171.18  																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 220.63/171.18  																																																																																																																																																																																																																							| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																						|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																						| (2607) aNaturalNumber0(xn) = all_72_1_100
% 220.63/171.18  																																																																																																																																																																																																																						| (2910) all_72_1_100 = all_16_2_18
% 220.63/171.18  																																																																																																																																																																																																																						|
% 220.63/171.18  																																																																																																																																																																																																																							| Combining equations (1244,2910) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																							| (1225) all_16_2_18 = 0
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																							| Combining equations (1225,2910) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																							| (1244) all_72_1_100 = 0
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																							| From (1244) and (2607) follows:
% 220.63/171.18  																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1116), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																							|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																							| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																								| From (1674) and (2552) follows:
% 220.63/171.18  																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 220.63/171.18  																																																																																																																																																																																																																								| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																							|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																							| (2555) aNaturalNumber0(xn) = all_52_2_87
% 220.63/171.18  																																																																																																																																																																																																																							| (2918) all_52_2_87 = all_14_2_15
% 220.63/171.18  																																																																																																																																																																																																																							|
% 220.63/171.18  																																																																																																																																																																																																																								| Combining equations (2918,1674) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																								| (2919) all_14_2_15 = 0
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																								| Simplifying 2919 yields:
% 220.63/171.18  																																																																																																																																																																																																																								| (1200) all_14_2_15 = 0
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																								| From (1674) and (2555) follows:
% 220.63/171.18  																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																								+-Applying beta-rule and splitting (730), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																								|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																								| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																									| From (1281) and (1969) follows:
% 220.63/171.18  																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 220.63/171.18  																																																																																																																																																																																																																									| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																								|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																								| (1972) aNaturalNumber0(xm) = all_12_0_10
% 220.63/171.18  																																																																																																																																																																																																																								| (2926) all_67_1_96 = all_12_0_10
% 220.63/171.18  																																																																																																																																																																																																																								|
% 220.63/171.18  																																																																																																																																																																																																																									| Combining equations (1242,2926) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																									| (1281) all_12_0_10 = 0
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																									| Combining equations (1281,2926) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																									| (1242) all_67_1_96 = 0
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																									| From (1281) and (1972) follows:
% 220.63/171.18  																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																									+-Applying beta-rule and splitting (776), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																									|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																									| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																										| From (1791) and (1977) follows:
% 220.63/171.18  																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 220.63/171.18  																																																																																																																																																																																																																										| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																									|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																									| (1980) aNaturalNumber0(xm) = all_72_2_101
% 220.63/171.18  																																																																																																																																																																																																																									| (2934) all_72_2_101 = all_37_3_64
% 220.63/171.18  																																																																																																																																																																																																																									|
% 220.63/171.18  																																																																																																																																																																																																																										| Combining equations (1791,2934) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																										| (1233) all_37_3_64 = 0
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																										| Combining equations (1233,2934) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																										| From (1791) and (1980) follows:
% 220.63/171.18  																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																										+-Applying beta-rule and splitting (708), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																										|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																										| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																											| From (1350) and (2136) follows:
% 220.63/171.18  																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 220.63/171.18  																																																																																																																																																																																																																											| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																										|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																										| (2139) aNaturalNumber0(xm) = all_24_0_28
% 220.63/171.18  																																																																																																																																																																																																																										| (2942) all_72_1_100 = all_24_0_28
% 220.63/171.18  																																																																																																																																																																																																																										|
% 220.63/171.18  																																																																																																																																																																																																																											| Combining equations (1244,2942) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																											| Combining equations (1350,2942) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																											| (1244) all_72_1_100 = 0
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																											| From (1350) and (2139) follows:
% 220.63/171.18  																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																											+-Applying beta-rule and splitting (600), into two cases.
% 220.63/171.18  																																																																																																																																																																																																																											|-Branch one:
% 220.63/171.18  																																																																																																																																																																																																																											| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																												| From (1791) and (2642) follows:
% 220.63/171.18  																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.18  																																																																																																																																																																																																																												|
% 220.63/171.18  																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 220.63/171.18  																																																																																																																																																																																																																												| (1311) $false
% 220.63/171.18  																																																																																																																																																																																																																												|
% 220.63/171.18  																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.18  																																																																																																																																																																																																																											|-Branch two:
% 220.63/171.18  																																																																																																																																																																																																																											| (2645) aNaturalNumber0(xp) = all_72_2_101
% 220.63/171.18  																																																																																																																																																																																																																											| (2950) all_72_2_101 = all_52_1_86
% 220.63/171.18  																																																																																																																																																																																																																											|
% 220.63/171.18  																																																																																																																																																																																																																												| Combining equations (1791,2950) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																												| (1238) all_52_1_86 = 0
% 220.63/171.18  																																																																																																																																																																																																																												|
% 220.63/171.18  																																																																																																																																																																																																																												| Combining equations (1238,2950) yields a new equation:
% 220.63/171.18  																																																																																																																																																																																																																												| (1791) all_72_2_101 = 0
% 220.63/171.18  																																																																																																																																																																																																																												|
% 220.63/171.18  																																																																																																																																																																																																																												| From (1791) and (2645) follows:
% 220.63/171.19  																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 220.63/171.19  																																																																																																																																																																																																																												|
% 220.63/171.19  																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1115), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																												|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																												| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 220.63/171.19  																																																																																																																																																																																																																												|
% 220.63/171.19  																																																																																																																																																																																																																													| From (1281) and (2374) follows:
% 220.63/171.19  																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 220.63/171.19  																																																																																																																																																																																																																													| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																												|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																												| (2377) aNaturalNumber0(xn) = all_12_0_10
% 220.63/171.19  																																																																																																																																																																																																																												| (2958) all_14_2_15 = all_12_0_10
% 220.63/171.19  																																																																																																																																																																																																																												|
% 220.63/171.19  																																																																																																																																																																																																																													| Combining equations (2958,1200) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																													| (2959) all_12_0_10 = 0
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																													| Simplifying 2959 yields:
% 220.63/171.19  																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																													| From (1281) and (2377) follows:
% 220.63/171.19  																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																													+-Applying beta-rule and splitting (804), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																													|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																													| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																														| From (1293) and (2962) follows:
% 220.63/171.19  																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 220.63/171.19  																																																																																																																																																																																																																														| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																													|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																													| (2965) aNaturalNumber0(xm) = all_47_2_83
% 220.63/171.19  																																																																																																																																																																																																																													| (2966) all_47_2_83 = all_22_1_26
% 220.63/171.19  																																																																																																																																																																																																																													|
% 220.63/171.19  																																																																																																																																																																																																																														| Combining equations (1293,2966) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																														| (1229) all_22_1_26 = 0
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																														| Combining equations (1229,2966) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																														| (1293) all_47_2_83 = 0
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																														| From (1293) and (2965) follows:
% 220.63/171.19  																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1152), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																														|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																														| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																															| From (1221) and (2081) follows:
% 220.63/171.19  																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.19  																																																																																																																																																																																																																															|
% 220.63/171.19  																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.63/171.19  																																																																																																																																																																																																																															| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																															|
% 220.63/171.19  																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																														|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																														| (2084) aNaturalNumber0(xn) = all_12_1_11
% 220.63/171.19  																																																																																																																																																																																																																														| (2974) all_12_1_11 = all_12_2_12
% 220.63/171.19  																																																																																																																																																																																																																														|
% 220.63/171.19  																																																																																																																																																																																																																															| From (1221) and (2084) follows:
% 220.63/171.19  																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.63/171.19  																																																																																																																																																																																																																															|
% 220.63/171.19  																																																																																																																																																																																																																															+-Applying beta-rule and splitting (490), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																															|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																															| (2178)  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 220.63/171.19  																																																																																																																																																																																																																															|
% 220.63/171.19  																																																																																																																																																																																																																																| From (1828) and (2178) follows:
% 220.63/171.19  																																																																																																																																																																																																																																| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																| Using (1284) and (2090) yields:
% 220.63/171.19  																																																																																																																																																																																																																																| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																															|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																															| (2181) aNaturalNumber0(all_0_9_9) = all_20_0_22
% 220.63/171.19  																																																																																																																																																																																																																															| (2980) all_20_0_22 = all_12_0_10
% 220.63/171.19  																																																																																																																																																																																																																															|
% 220.63/171.19  																																																																																																																																																																																																																																| Combining equations (1828,2980) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																| (1281) all_12_0_10 = 0
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																| Combining equations (1281,2980) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																| (1828) all_20_0_22 = 0
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																| From (1828) and (2181) follows:
% 220.63/171.19  																																																																																																																																																																																																																																| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1136), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																																|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																																| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																	| From (1292) and (2984) follows:
% 220.63/171.19  																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 220.63/171.19  																																																																																																																																																																																																																																	| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																																|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																																| (2987) aNaturalNumber0(xn) = all_16_0_16
% 220.63/171.19  																																																																																																																																																																																																																																| (2988) all_16_0_16 = all_12_2_12
% 220.63/171.19  																																																																																																																																																																																																																																|
% 220.63/171.19  																																																																																																																																																																																																																																	| Combining equations (1292,2988) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																	| (1223) all_12_2_12 = 0
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																	| Combining equations (1223,2988) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																	| From (1292) and (2987) follows:
% 220.63/171.19  																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (601), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																																	|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																																	| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																		| From (1790) and (2506) follows:
% 220.63/171.19  																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 220.63/171.19  																																																																																																																																																																																																																																		| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																																	|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																																	| (2509) aNaturalNumber0(xp) = all_62_2_94
% 220.63/171.19  																																																																																																																																																																																																																																	| (2996) all_62_2_94 = all_52_1_86
% 220.63/171.19  																																																																																																																																																																																																																																	|
% 220.63/171.19  																																																																																																																																																																																																																																		| Combining equations (2996,1790) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																		| (2997) all_52_1_86 = 0
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																		| Simplifying 2997 yields:
% 220.63/171.19  																																																																																																																																																																																																																																		| (1238) all_52_1_86 = 0
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																		| From (1790) and (2509) follows:
% 220.63/171.19  																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1069), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																																		|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																																		| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																			| From (1237) and (2490) follows:
% 220.63/171.19  																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 220.63/171.19  																																																																																																																																																																																																																																			| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																																		|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																																		| (2493) aNaturalNumber0(xn) = all_47_1_82
% 220.63/171.19  																																																																																																																																																																																																																																		| (3004) all_47_1_82 = all_18_2_21
% 220.63/171.19  																																																																																																																																																																																																																																		|
% 220.63/171.19  																																																																																																																																																																																																																																			| Combining equations (1237,3004) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																			| (1226) all_18_2_21 = 0
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																			| Combining equations (1226,3004) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																			| (1237) all_47_1_82 = 0
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																			| From (1237) and (2493) follows:
% 220.63/171.19  																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (966), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																																			|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																																			| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																				| From (1282) and (2210) follows:
% 220.63/171.19  																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.19  																																																																																																																																																																																																																																				|
% 220.63/171.19  																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 220.63/171.19  																																																																																																																																																																																																																																				| (1311) $false
% 220.63/171.19  																																																																																																																																																																																																																																				|
% 220.63/171.19  																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.63/171.19  																																																																																																																																																																																																																																			|-Branch two:
% 220.63/171.19  																																																																																																																																																																																																																																			| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.63/171.19  																																																																																																																																																																																																																																			| (3012) all_62_1_93 = all_24_2_30
% 220.63/171.19  																																																																																																																																																																																																																																			|
% 220.63/171.19  																																																																																																																																																																																																																																				| Combining equations (1240,3012) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																				| (1282) all_24_2_30 = 0
% 220.63/171.19  																																																																																																																																																																																																																																				|
% 220.63/171.19  																																																																																																																																																																																																																																				| Combining equations (1282,3012) yields a new equation:
% 220.63/171.19  																																																																																																																																																																																																																																				| (1240) all_62_1_93 = 0
% 220.63/171.19  																																																																																																																																																																																																																																				|
% 220.63/171.19  																																																																																																																																																																																																																																				| From (1282) and (2213) follows:
% 220.63/171.19  																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 220.63/171.19  																																																																																																																																																																																																																																				|
% 220.63/171.19  																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1080), into two cases.
% 220.63/171.19  																																																																																																																																																																																																																																				|-Branch one:
% 220.63/171.19  																																																																																																																																																																																																																																				| (3016)  ~ (aNaturalNumber0(sz00) = all_16_2_18)
% 220.63/171.19  																																																																																																																																																																																																																																				|
% 220.63/171.19  																																																																																																																																																																																																																																					| From (1225) and (3016) follows:
% 220.63/171.19  																																																																																																																																																																																																																																					| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.63/171.19  																																																																																																																																																																																																																																					|
% 220.63/171.19  																																																																																																																																																																																																																																					| Using (26) and (2070) yields:
% 220.63/171.20  																																																																																																																																																																																																																																					| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																					|
% 220.63/171.20  																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																				|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																				| (3019) aNaturalNumber0(sz00) = all_16_2_18
% 220.63/171.20  																																																																																																																																																																																																																																				| (1225) all_16_2_18 = 0
% 220.63/171.20  																																																																																																																																																																																																																																				|
% 220.63/171.20  																																																																																																																																																																																																																																					| From (1225) and (3019) follows:
% 220.63/171.20  																																																																																																																																																																																																																																					| (26) aNaturalNumber0(sz00) = 0
% 220.63/171.20  																																																																																																																																																																																																																																					|
% 220.63/171.20  																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (849), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																					|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																					| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 220.63/171.20  																																																																																																																																																																																																																																					|
% 220.63/171.20  																																																																																																																																																																																																																																						| From (848) and (2268) follows:
% 220.63/171.20  																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																						|
% 220.63/171.20  																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 220.63/171.20  																																																																																																																																																																																																																																						| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																						|
% 220.63/171.20  																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																					|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																					| (2271) aNaturalNumber0(xn) = all_16_1_17
% 220.63/171.20  																																																																																																																																																																																																																																					| (848) all_16_1_17 = 0
% 220.63/171.20  																																																																																																																																																																																																																																					|
% 220.63/171.20  																																																																																																																																																																																																																																						| From (848) and (2271) follows:
% 220.63/171.20  																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.63/171.20  																																																																																																																																																																																																																																						|
% 220.63/171.20  																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (785), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																						|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																						| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 220.63/171.20  																																																																																																																																																																																																																																						|
% 220.63/171.20  																																																																																																																																																																																																																																							| From (1283) and (3028) follows:
% 220.63/171.20  																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																							|
% 220.63/171.20  																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 220.63/171.20  																																																																																																																																																																																																																																							| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																							|
% 220.63/171.20  																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																						|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																						| (3031) aNaturalNumber0(xm) = all_26_2_33
% 220.63/171.20  																																																																																																																																																																																																																																						| (3032) all_37_3_64 = all_26_2_33
% 220.63/171.20  																																																																																																																																																																																																																																						|
% 220.63/171.20  																																																																																																																																																																																																																																							| Combining equations (1233,3032) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																							| (1283) all_26_2_33 = 0
% 220.63/171.20  																																																																																																																																																																																																																																							|
% 220.63/171.20  																																																																																																																																																																																																																																							| From (1283) and (3031) follows:
% 220.63/171.20  																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 220.63/171.20  																																																																																																																																																																																																																																							|
% 220.63/171.20  																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (788), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																							|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																							| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 220.63/171.20  																																																																																																																																																																																																																																							|
% 220.63/171.20  																																																																																																																																																																																																																																								| From (1674) and (3035) follows:
% 220.63/171.20  																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 220.63/171.20  																																																																																																																																																																																																																																								| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																							|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																							| (3038) aNaturalNumber0(xm) = all_52_2_87
% 220.63/171.20  																																																																																																																																																																																																																																							| (3039) all_52_2_87 = all_37_3_64
% 220.63/171.20  																																																																																																																																																																																																																																							|
% 220.63/171.20  																																																																																																																																																																																																																																								| Combining equations (3039,1674) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																								| (3040) all_37_3_64 = 0
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																								| Simplifying 3040 yields:
% 220.63/171.20  																																																																																																																																																																																																																																								| (1233) all_37_3_64 = 0
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																								| From (1674) and (3038) follows:
% 220.63/171.20  																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (946), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																								|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																								| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																									| From (1242) and (2334) follows:
% 220.63/171.20  																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 220.63/171.20  																																																																																																																																																																																																																																									| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																								|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																								| (2337) aNaturalNumber0(xn) = all_67_1_96
% 220.63/171.20  																																																																																																																																																																																																																																								| (3047) all_77_1_104 = all_67_1_96
% 220.63/171.20  																																																																																																																																																																																																																																								|
% 220.63/171.20  																																																																																																																																																																																																																																									| Combining equations (1246,3047) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																									| (1242) all_67_1_96 = 0
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																									| Combining equations (1242,3047) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																									| (1246) all_77_1_104 = 0
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																									| From (1242) and (2337) follows:
% 220.63/171.20  																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (405), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																									|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																									| (2755)  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																										| From (1790) and (2755) follows:
% 220.63/171.20  																																																																																																																																																																																																																																										| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																										| Using (1295) and (2129) yields:
% 220.63/171.20  																																																																																																																																																																																																																																										| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																									|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																									| (2758) aNaturalNumber0(all_0_7_7) = all_62_2_94
% 220.63/171.20  																																																																																																																																																																																																																																									| (3055) all_62_2_94 = all_47_2_83
% 220.63/171.20  																																																																																																																																																																																																																																									|
% 220.63/171.20  																																																																																																																																																																																																																																										| Combining equations (3055,1790) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																										| (3056) all_47_2_83 = 0
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																										| Simplifying 3056 yields:
% 220.63/171.20  																																																																																																																																																																																																																																										| (1293) all_47_2_83 = 0
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																										| From (1790) and (2758) follows:
% 220.63/171.20  																																																																																																																																																																																																																																										| (1295) aNaturalNumber0(all_0_7_7) = 0
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (952), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																										|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																										| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																											| From (848) and (2268) follows:
% 220.63/171.20  																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 220.63/171.20  																																																																																																																																																																																																																																											| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																										|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																										| (2271) aNaturalNumber0(xn) = all_16_1_17
% 220.63/171.20  																																																																																																																																																																																																																																										| (3063) all_77_1_104 = all_16_1_17
% 220.63/171.20  																																																																																																																																																																																																																																										|
% 220.63/171.20  																																																																																																																																																																																																																																											| Combining equations (1246,3063) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																											| (848) all_16_1_17 = 0
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																											| Combining equations (848,3063) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																											| (1246) all_77_1_104 = 0
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																											| From (848) and (2271) follows:
% 220.63/171.20  																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1139), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																											|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																											| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																												| From (1282) and (2210) follows:
% 220.63/171.20  																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 220.63/171.20  																																																																																																																																																																																																																																												| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																											|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																											| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.63/171.20  																																																																																																																																																																																																																																											| (3071) all_24_2_30 = all_12_2_12
% 220.63/171.20  																																																																																																																																																																																																																																											|
% 220.63/171.20  																																																																																																																																																																																																																																												| Combining equations (1282,3071) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																												| (1223) all_12_2_12 = 0
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																												| Combining equations (1223,3071) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																												| From (1282) and (2213) follows:
% 220.63/171.20  																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (937), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																												|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																												| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																													| From (1294) and (1953) follows:
% 220.63/171.20  																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																													|
% 220.63/171.20  																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 220.63/171.20  																																																																																																																																																																																																																																													| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																													|
% 220.63/171.20  																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																												|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																												| (1956) aNaturalNumber0(xn) = all_77_2_105
% 220.63/171.20  																																																																																																																																																																																																																																												| (3079) all_77_1_104 = all_77_2_105
% 220.63/171.20  																																																																																																																																																																																																																																												|
% 220.63/171.20  																																																																																																																																																																																																																																													| Combining equations (1246,3079) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 220.63/171.20  																																																																																																																																																																																																																																													|
% 220.63/171.20  																																																																																																																																																																																																																																													| Combining equations (1294,3079) yields a new equation:
% 220.63/171.20  																																																																																																																																																																																																																																													| (1246) all_77_1_104 = 0
% 220.63/171.20  																																																																																																																																																																																																																																													|
% 220.63/171.20  																																																																																																																																																																																																																																													| From (1294) and (1956) follows:
% 220.63/171.20  																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.63/171.20  																																																																																																																																																																																																																																													|
% 220.63/171.20  																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1148), into two cases.
% 220.63/171.20  																																																																																																																																																																																																																																													|-Branch one:
% 220.63/171.20  																																																																																																																																																																																																																																													| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 220.63/171.20  																																																																																																																																																																																																																																													|
% 220.63/171.20  																																																																																																																																																																																																																																														| From (1228) and (2055) follows:
% 220.63/171.20  																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.20  																																																																																																																																																																																																																																														|
% 220.63/171.20  																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 220.63/171.20  																																																																																																																																																																																																																																														| (1311) $false
% 220.63/171.20  																																																																																																																																																																																																																																														|
% 220.63/171.20  																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.63/171.20  																																																																																																																																																																																																																																													|-Branch two:
% 220.63/171.20  																																																																																																																																																																																																																																													| (2058) aNaturalNumber0(xn) = all_20_1_23
% 220.63/171.21  																																																																																																																																																																																																																																													| (3087) all_20_1_23 = all_12_2_12
% 220.63/171.21  																																																																																																																																																																																																																																													|
% 220.63/171.21  																																																																																																																																																																																																																																														| Combining equations (1228,3087) yields a new equation:
% 220.63/171.21  																																																																																																																																																																																																																																														| (1223) all_12_2_12 = 0
% 220.63/171.21  																																																																																																																																																																																																																																														|
% 220.63/171.21  																																																																																																																																																																																																																																														| Combining equations (1223,3087) yields a new equation:
% 220.63/171.21  																																																																																																																																																																																																																																														| (1228) all_20_1_23 = 0
% 220.63/171.21  																																																																																																																																																																																																																																														|
% 220.63/171.21  																																																																																																																																																																																																																																														| From (1228) and (2058) follows:
% 220.63/171.21  																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.63/171.21  																																																																																																																																																																																																																																														|
% 220.63/171.21  																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1040), into two cases.
% 220.63/171.21  																																																																																																																																																																																																																																														|-Branch one:
% 220.63/171.21  																																																																																																																																																																																																																																														| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.63/171.21  																																																																																																																																																																																																																																														|
% 220.63/171.21  																																																																																																																																																																																																																																															| From (1282) and (2210) follows:
% 220.63/171.21  																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.63/171.21  																																																																																																																																																																																																																																															| (1311) $false
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.63/171.21  																																																																																																																																																																																																																																														|-Branch two:
% 220.63/171.21  																																																																																																																																																																																																																																														| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.63/171.21  																																																																																																																																																																																																																																														| (3095) all_37_4_65 = all_24_2_30
% 220.63/171.21  																																																																																																																																																																																																																																														|
% 220.63/171.21  																																																																																																																																																																																																																																															| Combining equations (1232,3095) yields a new equation:
% 220.63/171.21  																																																																																																																																																																																																																																															| (1282) all_24_2_30 = 0
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																															| Combining equations (1282,3095) yields a new equation:
% 220.63/171.21  																																																																																																																																																																																																																																															| (1232) all_37_4_65 = 0
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																															| From (1282) and (2213) follows:
% 220.63/171.21  																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (594), into two cases.
% 220.63/171.21  																																																																																																																																																																																																																																															|-Branch one:
% 220.63/171.21  																																																																																																																																																																																																																																															| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																																| From (1283) and (2007) follows:
% 220.63/171.21  																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.63/171.21  																																																																																																																																																																																																																																																|
% 220.63/171.21  																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 220.63/171.21  																																																																																																																																																																																																																																																| (1311) $false
% 220.63/171.21  																																																																																																																																																																																																																																																|
% 220.63/171.21  																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.63/171.21  																																																																																																																																																																																																																																															|-Branch two:
% 220.63/171.21  																																																																																																																																																																																																																																															| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.63/171.21  																																																																																																																																																																																																																																															| (3103) all_57_3_91 = all_26_2_33
% 220.63/171.21  																																																																																																																																																																																																																																															|
% 220.63/171.21  																																																																																																																																																																																																																																																| Combining equations (2199,3103) yields a new equation:
% 220.63/171.21  																																																																																																																																																																																																																																																| (1283) all_26_2_33 = 0
% 220.63/171.21  																																																																																																																																																																																																																																																|
% 220.63/171.21  																																																																																																																																																																																																																																																| From (1283) and (2010) follows:
% 220.63/171.21  																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 220.63/171.21  																																																																																																																																																																																																																																																|
% 220.63/171.21  																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (753), into two cases.
% 220.63/171.21  																																																																																																																																																																																																																																																|-Branch one:
% 220.63/171.21  																																																																																																																																																																																																																																																| (3106)  ~ (aNaturalNumber0(sz00) = all_39_7_73)
% 220.63/171.21  																																																																																																																																																																																																																																																|
% 220.63/171.21  																																																																																																																																																																																																																																																	| From (1236) and (3106) follows:
% 220.63/171.21  																																																																																																																																																																																																																																																	| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.63/171.21  																																																																																																																																																																																																																																																	|
% 220.63/171.21  																																																																																																																																																																																																																																																	| Using (26) and (2070) yields:
% 220.63/171.21  																																																																																																																																																																																																																																																	| (1311) $false
% 220.63/171.21  																																																																																																																																																																																																																																																	|
% 220.63/171.21  																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.63/171.21  																																																																																																																																																																																																																																																|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																| (3109) aNaturalNumber0(sz00) = all_39_7_73
% 220.99/171.21  																																																																																																																																																																																																																																																| (1236) all_39_7_73 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																|
% 220.99/171.21  																																																																																																																																																																																																																																																	| From (1236) and (3109) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																	| (26) aNaturalNumber0(sz00) = 0
% 220.99/171.21  																																																																																																																																																																																																																																																	|
% 220.99/171.21  																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (901), into two cases.
% 220.99/171.21  																																																																																																																																																																																																																																																	|-Branch one:
% 220.99/171.21  																																																																																																																																																																																																																																																	| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 220.99/171.21  																																																																																																																																																																																																																																																	|
% 220.99/171.21  																																																																																																																																																																																																																																																		| From (1293) and (2962) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (1311) $false
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.99/171.21  																																																																																																																																																																																																																																																	|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																	| (2965) aNaturalNumber0(xm) = all_47_2_83
% 220.99/171.21  																																																																																																																																																																																																																																																	| (3116) all_47_2_83 = all_12_1_11
% 220.99/171.21  																																																																																																																																																																																																																																																	|
% 220.99/171.21  																																																																																																																																																																																																																																																		| Combining equations (1293,3116) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (1221) all_12_1_11 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																		| Combining equations (1221,3116) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																		| From (1293) and (2965) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1086), into two cases.
% 220.99/171.21  																																																																																																																																																																																																																																																		|-Branch one:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																			| From (1292) and (2984) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (1311) $false
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.99/171.21  																																																																																																																																																																																																																																																		|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																		| (2987) aNaturalNumber0(xn) = all_16_0_16
% 220.99/171.21  																																																																																																																																																																																																																																																		| (3124) all_16_0_16 = all_16_2_18
% 220.99/171.21  																																																																																																																																																																																																																																																		|
% 220.99/171.21  																																																																																																																																																																																																																																																			| Combining equations (1292,3124) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (1225) all_16_2_18 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																			| Combining equations (1225,3124) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																			| From (1292) and (2987) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (844), into two cases.
% 220.99/171.21  																																																																																																																																																																																																																																																			|-Branch one:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																				| From (1282) and (2382) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (1311) $false
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.99/171.21  																																																																																																																																																																																																																																																			|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																			| (2385) aNaturalNumber0(xm) = all_24_2_30
% 220.99/171.21  																																																																																																																																																																																																																																																			| (3132) all_24_2_30 = all_18_1_20
% 220.99/171.21  																																																																																																																																																																																																																																																			|
% 220.99/171.21  																																																																																																																																																																																																																																																				| Combining equations (1282,3132) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (1227) all_18_1_20 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																				| Combining equations (1227,3132) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (1282) all_24_2_30 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																				| From (1282) and (2385) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1060), into two cases.
% 220.99/171.21  																																																																																																																																																																																																																																																				|-Branch one:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																					| From (1294) and (1953) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (1311) $false
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.99/171.21  																																																																																																																																																																																																																																																				|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																				| (1956) aNaturalNumber0(xn) = all_77_2_105
% 220.99/171.21  																																																																																																																																																																																																																																																				| (3140) all_77_2_105 = all_18_2_21
% 220.99/171.21  																																																																																																																																																																																																																																																				|
% 220.99/171.21  																																																																																																																																																																																																																																																					| Combining equations (1294,3140) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (1226) all_18_2_21 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																					| Combining equations (1226,3140) yields a new equation:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																					| From (1294) and (1956) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (353), into two cases.
% 220.99/171.21  																																																																																																																																																																																																																																																					|-Branch one:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (3144)  ~ (aNaturalNumber0(sz00) = all_57_2_90)
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																						| From (1789) and (3144) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																						| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.99/171.21  																																																																																																																																																																																																																																																						|
% 220.99/171.21  																																																																																																																																																																																																																																																						| Using (26) and (2070) yields:
% 220.99/171.21  																																																																																																																																																																																																																																																						| (1311) $false
% 220.99/171.21  																																																																																																																																																																																																																																																						|
% 220.99/171.21  																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.99/171.21  																																																																																																																																																																																																																																																					|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																					| (3147) aNaturalNumber0(sz00) = all_57_2_90
% 220.99/171.21  																																																																																																																																																																																																																																																					| (1789) all_57_2_90 = 0
% 220.99/171.21  																																																																																																																																																																																																																																																					|
% 220.99/171.21  																																																																																																																																																																																																																																																						| From (1789) and (3147) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																						| (26) aNaturalNumber0(sz00) = 0
% 220.99/171.21  																																																																																																																																																																																																																																																						|
% 220.99/171.21  																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1037), into two cases.
% 220.99/171.21  																																																																																																																																																																																																																																																						|-Branch one:
% 220.99/171.21  																																																																																																																																																																																																																																																						| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 220.99/171.21  																																																																																																																																																																																																																																																						|
% 220.99/171.21  																																																																																																																																																																																																																																																							| From (1292) and (2984) follows:
% 220.99/171.21  																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.21  																																																																																																																																																																																																																																																							|
% 220.99/171.21  																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 220.99/171.21  																																																																																																																																																																																																																																																							| (1311) $false
% 220.99/171.21  																																																																																																																																																																																																																																																							|
% 220.99/171.21  																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.99/171.21  																																																																																																																																																																																																																																																						|-Branch two:
% 220.99/171.21  																																																																																																																																																																																																																																																						| (2987) aNaturalNumber0(xn) = all_16_0_16
% 220.99/171.22  																																																																																																																																																																																																																																																						| (3154) all_37_4_65 = all_16_0_16
% 220.99/171.22  																																																																																																																																																																																																																																																						|
% 220.99/171.22  																																																																																																																																																																																																																																																							| Combining equations (1232,3154) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																							| (1292) all_16_0_16 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																							|
% 220.99/171.22  																																																																																																																																																																																																																																																							| From (1292) and (2987) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																							|
% 220.99/171.22  																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (458), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																							|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																							| (2467)  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 220.99/171.22  																																																																																																																																																																																																																																																							|
% 220.99/171.22  																																																																																																																																																																																																																																																								| From (1293) and (2467) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																								| Using (1284) and (2090) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																							|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																							| (2470) aNaturalNumber0(all_0_9_9) = all_47_2_83
% 220.99/171.22  																																																																																																																																																																																																																																																							| (3161) all_47_2_83 = all_26_2_33
% 220.99/171.22  																																																																																																																																																																																																																																																							|
% 220.99/171.22  																																																																																																																																																																																																																																																								| Combining equations (1293,3161) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (1283) all_26_2_33 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																								| Combining equations (1283,3161) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (1293) all_47_2_83 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																								| From (1293) and (2470) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1028), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																								|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																									| From (1218) and (3165) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																								|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																								| (3168) aNaturalNumber0(xn) = all_14_1_14
% 220.99/171.22  																																																																																																																																																																																																																																																								| (3169) all_39_8_74 = all_14_1_14
% 220.99/171.22  																																																																																																																																																																																																																																																								|
% 220.99/171.22  																																																																																																																																																																																																																																																									| Combining equations (1179,3169) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1218) all_14_1_14 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																									| Combining equations (1218,3169) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1179) all_39_8_74 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																									| From (1218) and (3168) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (374), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																									|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																										| Using (1775) and (1780) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																										| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																										|
% 220.99/171.22  																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																									|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1775) aNaturalNumber0(all_0_3_3) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																									| (1787) all_20_2_24 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																									|
% 220.99/171.22  																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1024), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																										|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																										| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 220.99/171.22  																																																																																																																																																																																																																																																										|
% 220.99/171.22  																																																																																																																																																																																																																																																											| From (1229) and (2891) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																											|
% 220.99/171.22  																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																											| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																											|
% 220.99/171.22  																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																										|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																										| (2894) aNaturalNumber0(xn) = all_22_1_26
% 220.99/171.22  																																																																																																																																																																																																																																																										| (3181) all_39_8_74 = all_22_1_26
% 220.99/171.22  																																																																																																																																																																																																																																																										|
% 220.99/171.22  																																																																																																																																																																																																																																																											| Combining equations (1179,3181) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																											| (1229) all_22_1_26 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																											|
% 220.99/171.22  																																																																																																																																																																																																																																																											| From (1229) and (2894) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																											|
% 220.99/171.22  																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (461), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																											|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																											| (3184)  ~ (aNaturalNumber0(xr) = all_24_2_30)
% 220.99/171.22  																																																																																																																																																																																																																																																											|
% 220.99/171.22  																																																																																																																																																																																																																																																												| From (1931)(1282) and (3184) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																												|
% 220.99/171.22  																																																																																																																																																																																																																																																												| Using (1665) and (1670) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																												| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																												|
% 220.99/171.22  																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																											|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																											| (3187) aNaturalNumber0(xr) = all_24_2_30
% 220.99/171.22  																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																											|
% 220.99/171.22  																																																																																																																																																																																																																																																												| From (1931)(1282) and (3187) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																												|
% 220.99/171.22  																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1012), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																												|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																												| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 220.99/171.22  																																																																																																																																																																																																																																																												|
% 220.99/171.22  																																																																																																																																																																																																																																																													| From (1293) and (2061) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																												|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																												| (2064) aNaturalNumber0(xn) = all_47_2_83
% 220.99/171.22  																																																																																																																																																																																																																																																												| (3194) all_47_2_83 = all_39_8_74
% 220.99/171.22  																																																																																																																																																																																																																																																												|
% 220.99/171.22  																																																																																																																																																																																																																																																													| Combining equations (1293,3194) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (1179) all_39_8_74 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																													| Combining equations (1179,3194) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (1293) all_47_2_83 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																													| From (1293) and (2064) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (968), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																													|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																														| From (1674) and (2552) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																													|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																													| (2555) aNaturalNumber0(xn) = all_52_2_87
% 220.99/171.22  																																																																																																																																																																																																																																																													| (3202) all_62_1_93 = all_52_2_87
% 220.99/171.22  																																																																																																																																																																																																																																																													|
% 220.99/171.22  																																																																																																																																																																																																																																																														| Combining equations (1240,3202) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (1674) all_52_2_87 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																														| Combining equations (1674,3202) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (1240) all_62_1_93 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																														| From (1674) and (2555) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (991), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																														|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																															| From (1282) and (2210) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																															|
% 220.99/171.22  																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																															|
% 220.99/171.22  																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																														|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																														| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.99/171.22  																																																																																																																																																																																																																																																														| (3210) all_57_1_89 = all_24_2_30
% 220.99/171.22  																																																																																																																																																																																																																																																														|
% 220.99/171.22  																																																																																																																																																																																																																																																															| Combining equations (980,3210) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (1282) all_24_2_30 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																															|
% 220.99/171.22  																																																																																																																																																																																																																																																															| Combining equations (1282,3210) yields a new equation:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (980) all_57_1_89 = 0
% 220.99/171.22  																																																																																																																																																																																																																																																															|
% 220.99/171.22  																																																																																																																																																																																																																																																															| From (1282) and (2213) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.99/171.22  																																																																																																																																																																																																																																																															|
% 220.99/171.22  																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (891), into two cases.
% 220.99/171.22  																																																																																																																																																																																																																																																															|-Branch one:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (3214)  ~ (aNaturalNumber0(sz00) = all_12_1_11)
% 220.99/171.22  																																																																																																																																																																																																																																																															|
% 220.99/171.22  																																																																																																																																																																																																																																																																| From (1221) and (3214) follows:
% 220.99/171.22  																																																																																																																																																																																																																																																																| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.99/171.22  																																																																																																																																																																																																																																																																|
% 220.99/171.22  																																																																																																																																																																																																																																																																| Using (26) and (2070) yields:
% 220.99/171.22  																																																																																																																																																																																																																																																																| (1311) $false
% 220.99/171.22  																																																																																																																																																																																																																																																																|
% 220.99/171.22  																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.99/171.22  																																																																																																																																																																																																																																																															|-Branch two:
% 220.99/171.22  																																																																																																																																																																																																																																																															| (3217) aNaturalNumber0(sz00) = all_12_1_11
% 220.99/171.23  																																																																																																																																																																																																																																																															| (1221) all_12_1_11 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																															|
% 220.99/171.23  																																																																																																																																																																																																																																																																| From (1221) and (3217) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																| (26) aNaturalNumber0(sz00) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																|
% 220.99/171.23  																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (988), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 220.99/171.23  																																																																																																																																																																																																																																																																|
% 220.99/171.23  																																																																																																																																																																																																																																																																	| From (1292) and (2984) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																	|
% 220.99/171.23  																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																	|
% 220.99/171.23  																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																| (2987) aNaturalNumber0(xn) = all_16_0_16
% 220.99/171.23  																																																																																																																																																																																																																																																																| (3224) all_57_1_89 = all_16_0_16
% 220.99/171.23  																																																																																																																																																																																																																																																																|
% 220.99/171.23  																																																																																																																																																																																																																																																																	| Combining equations (980,3224) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																	|
% 220.99/171.23  																																																																																																																																																																																																																																																																	| From (1292) and (2987) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																	|
% 220.99/171.23  																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (562), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																	|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.99/171.23  																																																																																																																																																																																																																																																																	|
% 220.99/171.23  																																																																																																																																																																																																																																																																		| From (1283) and (2007) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																	|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.99/171.23  																																																																																																																																																																																																																																																																	| (3231) all_72_3_102 = all_26_2_33
% 220.99/171.23  																																																																																																																																																																																																																																																																	|
% 220.99/171.23  																																																																																																																																																																																																																																																																		| Combining equations (1243,3231) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (1283) all_26_2_33 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																		| Combining equations (1283,3231) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (1243) all_72_3_102 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																		| From (1283) and (2010) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (749), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																		|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																			| From (1281) and (1969) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																		|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (1972) aNaturalNumber0(xm) = all_12_0_10
% 220.99/171.23  																																																																																																																																																																																																																																																																		| (3239) all_47_1_82 = all_12_0_10
% 220.99/171.23  																																																																																																																																																																																																																																																																		|
% 220.99/171.23  																																																																																																																																																																																																																																																																			| Combining equations (1237,3239) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (1281) all_12_0_10 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																			| Combining equations (1281,3239) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (1237) all_47_1_82 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																			| From (1281) and (1972) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (443), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																			|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																				| From (1283) and (2007) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																				|
% 220.99/171.23  																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																				| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																				|
% 220.99/171.23  																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																			|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.99/171.23  																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																			|
% 220.99/171.23  																																																																																																																																																																																																																																																																				| From (1283) and (2010) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																				|
% 220.99/171.23  																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (734), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																				|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																				| (3249)  ~ (aNaturalNumber0(sz10) = all_47_1_82)
% 220.99/171.23  																																																																																																																																																																																																																																																																				|
% 220.99/171.23  																																																																																																																																																																																																																																																																					| From (1237) and (3249) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																					| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																					|
% 220.99/171.23  																																																																																																																																																																																																																																																																					| Using (61) and (1994) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																					| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																					|
% 220.99/171.23  																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																				|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																				| (3252) aNaturalNumber0(sz10) = all_47_1_82
% 220.99/171.23  																																																																																																																																																																																																																																																																				| (1237) all_47_1_82 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																				|
% 220.99/171.23  																																																																																																																																																																																																																																																																					| From (1237) and (3252) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																					| (61) aNaturalNumber0(sz10) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																					|
% 220.99/171.23  																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (401), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																					|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																					| (3255)  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 220.99/171.23  																																																																																																																																																																																																																																																																					|
% 220.99/171.23  																																																																																																																																																																																																																																																																						| From (1830) and (3255) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																						| Using (1295) and (2129) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																					|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																					| (3258) aNaturalNumber0(all_0_7_7) = all_82_2_109
% 220.99/171.23  																																																																																																																																																																																																																																																																					| (3259) all_82_2_109 = all_47_2_83
% 220.99/171.23  																																																																																																																																																																																																																																																																					|
% 220.99/171.23  																																																																																																																																																																																																																																																																						| Combining equations (1830,3259) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (1293) all_47_2_83 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																						| Combining equations (1293,3259) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (1830) all_82_2_109 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																						| From (1830) and (3258) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (1295) aNaturalNumber0(all_0_7_7) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (548), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																						|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																							| From (1281) and (2039) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																						|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (2042) aNaturalNumber0(xp) = all_12_0_10
% 220.99/171.23  																																																																																																																																																																																																																																																																						| (3267) all_77_3_106 = all_12_0_10
% 220.99/171.23  																																																																																																																																																																																																																																																																						|
% 220.99/171.23  																																																																																																																																																																																																																																																																							| Combining equations (1245,3267) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (1281) all_12_0_10 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																							| Combining equations (1281,3267) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (1245) all_77_3_106 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																							| From (1281) and (2042) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1151), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																							|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																								| From (1218) and (3165) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																							|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (3168) aNaturalNumber0(xn) = all_14_1_14
% 220.99/171.23  																																																																																																																																																																																																																																																																							| (3275) all_14_1_14 = all_12_2_12
% 220.99/171.23  																																																																																																																																																																																																																																																																							|
% 220.99/171.23  																																																																																																																																																																																																																																																																								| Combining equations (3275,1218) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (1222) all_12_2_12 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																								| Simplifying 1222 yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (1223) all_12_2_12 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																								| From (1218) and (3168) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1127), into two cases.
% 220.99/171.23  																																																																																																																																																																																																																																																																								|-Branch one:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																									| From (1221) and (2081) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.23  																																																																																																																																																																																																																																																																									|
% 220.99/171.23  																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																									| (1311) $false
% 220.99/171.23  																																																																																																																																																																																																																																																																									|
% 220.99/171.23  																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.99/171.23  																																																																																																																																																																																																																																																																								|-Branch two:
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (2084) aNaturalNumber0(xn) = all_12_1_11
% 220.99/171.23  																																																																																																																																																																																																																																																																								| (3283) all_14_2_15 = all_12_1_11
% 220.99/171.23  																																																																																																																																																																																																																																																																								|
% 220.99/171.23  																																																																																																																																																																																																																																																																									| Combining equations (3283,1200) yields a new equation:
% 220.99/171.23  																																																																																																																																																																																																																																																																									| (3284) all_12_1_11 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																									|
% 220.99/171.23  																																																																																																																																																																																																																																																																									| Simplifying 3284 yields:
% 220.99/171.23  																																																																																																																																																																																																																																																																									| (1221) all_12_1_11 = 0
% 220.99/171.23  																																																																																																																																																																																																																																																																									|
% 220.99/171.23  																																																																																																																																																																																																																																																																									| From (1221) and (2084) follows:
% 220.99/171.23  																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																									|
% 220.99/171.24  																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1120), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																									|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																									| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 220.99/171.24  																																																																																																																																																																																																																																																																									|
% 220.99/171.24  																																																																																																																																																																																																																																																																										| From (1236) and (2522) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																									|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																									| (2525) aNaturalNumber0(xn) = all_39_7_73
% 220.99/171.24  																																																																																																																																																																																																																																																																									| (3291) all_39_7_73 = all_14_2_15
% 220.99/171.24  																																																																																																																																																																																																																																																																									|
% 220.99/171.24  																																																																																																																																																																																																																																																																										| Combining equations (1236,3291) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (1200) all_14_2_15 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																										| Combining equations (1200,3291) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (1236) all_39_7_73 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																										| From (1236) and (2525) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (925), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																										|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																											| From (1233) and (3295) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																										|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (3298) aNaturalNumber0(xn) = all_37_3_64
% 220.99/171.24  																																																																																																																																																																																																																																																																										| (3299) all_82_1_108 = all_37_3_64
% 220.99/171.24  																																																																																																																																																																																																																																																																										|
% 220.99/171.24  																																																																																																																																																																																																																																																																											| Combining equations (1249,3299) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (1233) all_37_3_64 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																											| Combining equations (1233,3299) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (1249) all_82_1_108 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																											| From (1233) and (3298) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (692), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																											|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																												| From (1282) and (2475) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																												|
% 220.99/171.24  																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																												|
% 220.99/171.24  																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																											|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (2478) aNaturalNumber0(xp) = all_24_2_30
% 220.99/171.24  																																																																																																																																																																																																																																																																											| (3307) all_24_1_29 = all_24_2_30
% 220.99/171.24  																																																																																																																																																																																																																																																																											|
% 220.99/171.24  																																																																																																																																																																																																																																																																												| Combining equations (1207,3307) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																												|
% 220.99/171.24  																																																																																																																																																																																																																																																																												| From (1282) and (2478) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																												|
% 220.99/171.24  																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (639), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																												|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 220.99/171.24  																																																																																																																																																																																																																																																																												|
% 220.99/171.24  																																																																																																																																																																																																																																																																													| From (1293) and (2159) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																												|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (2162) aNaturalNumber0(xp) = all_47_2_83
% 220.99/171.24  																																																																																																																																																																																																																																																																												| (3314) all_47_2_83 = all_39_6_72
% 220.99/171.24  																																																																																																																																																																																																																																																																												|
% 220.99/171.24  																																																																																																																																																																																																																																																																													| Combining equations (1293,3314) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (629) all_39_6_72 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																													| Combining equations (629,3314) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (1293) all_47_2_83 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																													| From (1293) and (2162) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1129), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																													|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (3318)  ~ (aNaturalNumber0(sz10) = all_12_2_12)
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																														| From (1223) and (3318) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																														|
% 220.99/171.24  																																																																																																																																																																																																																																																																														| Using (61) and (1994) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																														| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																														|
% 220.99/171.24  																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																													|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (3321) aNaturalNumber0(sz10) = all_12_2_12
% 220.99/171.24  																																																																																																																																																																																																																																																																													| (1223) all_12_2_12 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																													|
% 220.99/171.24  																																																																																																																																																																																																																																																																														| From (1223) and (3321) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																														| (61) aNaturalNumber0(sz10) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																														|
% 220.99/171.24  																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (963), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																														|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																														| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 220.99/171.24  																																																																																																																																																																																																																																																																														|
% 220.99/171.24  																																																																																																																																																																																																																																																																															| From (1292) and (2984) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																															|
% 220.99/171.24  																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																															|
% 220.99/171.24  																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																														|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																														| (2987) aNaturalNumber0(xn) = all_16_0_16
% 220.99/171.24  																																																																																																																																																																																																																																																																														| (3328) all_62_1_93 = all_16_0_16
% 220.99/171.24  																																																																																																																																																																																																																																																																														|
% 220.99/171.24  																																																																																																																																																																																																																																																																															| Combining equations (1240,3328) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (1292) all_16_0_16 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																															|
% 220.99/171.24  																																																																																																																																																																																																																																																																															| From (1292) and (2987) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																															|
% 220.99/171.24  																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (513), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																															|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (3331)  ~ (aNaturalNumber0(xk) = all_47_2_83)
% 220.99/171.24  																																																																																																																																																																																																																																																																															|
% 220.99/171.24  																																																																																																																																																																																																																																																																																| From (1293) and (3331) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																| Using (1665) and (1670) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																															|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (3334) aNaturalNumber0(xk) = all_47_2_83
% 220.99/171.24  																																																																																																																																																																																																																																																																															| (3335) all_52_2_87 = all_47_2_83
% 220.99/171.24  																																																																																																																																																																																																																																																																															|
% 220.99/171.24  																																																																																																																																																																																																																																																																																| Combining equations (3335,1674) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (3056) all_47_2_83 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																| Simplifying 3056 yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (1293) all_47_2_83 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																| From (1293) and (3334) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (1665) aNaturalNumber0(xk) = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (653), into two cases.
% 220.99/171.24  																																																																																																																																																																																																																																																																																|-Branch one:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| From (1294) and (3339) follows:
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.24  																																																																																																																																																																																																																																																																																	|
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| (1311) $false
% 220.99/171.24  																																																																																																																																																																																																																																																																																	|
% 220.99/171.24  																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.99/171.24  																																																																																																																																																																																																																																																																																|-Branch two:
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (3342) aNaturalNumber0(xp) = all_77_2_105
% 220.99/171.24  																																																																																																																																																																																																																																																																																| (3343) all_77_2_105 = all_37_2_63
% 220.99/171.24  																																																																																																																																																																																																																																																																																|
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| Combining equations (1294,3343) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| (1195) all_37_2_63 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																																	|
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| Combining equations (1195,3343) yields a new equation:
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| (1294) all_77_2_105 = 0
% 220.99/171.24  																																																																																																																																																																																																																																																																																	|
% 220.99/171.24  																																																																																																																																																																																																																																																																																	| From (1294) and (3342) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																	|
% 220.99/171.25  																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (499), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																	|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																	| (2232)  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 220.99/171.25  																																																																																																																																																																																																																																																																																	|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| From (1350) and (2232) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| Using (1284) and (2090) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																	|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																	| (2235) aNaturalNumber0(all_0_9_9) = all_24_0_28
% 220.99/171.25  																																																																																																																																																																																																																																																																																	| (3351) all_24_0_28 = all_12_0_10
% 220.99/171.25  																																																																																																																																																																																																																																																																																	|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| Combining equations (1350,3351) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| Combining equations (1281,3351) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| From (1350) and (2235) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (1284) aNaturalNumber0(all_0_9_9) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (928), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| From (1227) and (1933) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (1936) aNaturalNumber0(xn) = all_18_1_20
% 220.99/171.25  																																																																																																																																																																																																																																																																																		| (3359) all_82_1_108 = all_18_1_20
% 220.99/171.25  																																																																																																																																																																																																																																																																																		|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| Combining equations (1249,3359) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (1227) all_18_1_20 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| Combining equations (1227,3359) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (1249) all_82_1_108 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| From (1227) and (1936) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (970), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| From (1242) and (2334) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (2337) aNaturalNumber0(xn) = all_67_1_96
% 220.99/171.25  																																																																																																																																																																																																																																																																																			| (3367) all_67_1_96 = all_62_1_93
% 220.99/171.25  																																																																																																																																																																																																																																																																																			|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| Combining equations (1242,3367) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (1240) all_62_1_93 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| Combining equations (1240,3367) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (1242) all_67_1_96 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| From (1242) and (2337) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1124), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| From (1227) and (1933) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (1936) aNaturalNumber0(xn) = all_18_1_20
% 220.99/171.25  																																																																																																																																																																																																																																																																																				| (3375) all_18_1_20 = all_14_2_15
% 220.99/171.25  																																																																																																																																																																																																																																																																																				|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| Combining equations (1227,3375) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (1200) all_14_2_15 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| Combining equations (1200,3375) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (1227) all_18_1_20 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| From (1227) and (1936) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1085), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| From (1293) and (2061) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (2064) aNaturalNumber0(xn) = all_47_2_83
% 220.99/171.25  																																																																																																																																																																																																																																																																																					| (3383) all_47_2_83 = all_16_2_18
% 220.99/171.25  																																																																																																																																																																																																																																																																																					|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| Combining equations (1293,3383) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (1225) all_16_2_18 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| Combining equations (1225,3383) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (1293) all_47_2_83 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| From (1293) and (2064) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (528), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| From (1293) and (2159) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (2162) aNaturalNumber0(xp) = all_47_2_83
% 220.99/171.25  																																																																																																																																																																																																																																																																																						| (3391) all_82_3_110 = all_47_2_83
% 220.99/171.25  																																																																																																																																																																																																																																																																																						|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| Combining equations (1247,3391) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (1293) all_47_2_83 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| Combining equations (1293,3391) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (1247) all_82_3_110 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| From (1293) and (2162) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (889), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| From (1221) and (2081) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (2084) aNaturalNumber0(xn) = all_12_1_11
% 220.99/171.25  																																																																																																																																																																																																																																																																																							| (1221) all_12_1_11 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																							|
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| From (1221) and (2084) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|
% 220.99/171.25  																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (627), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| From (1281) and (2039) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| (2042) aNaturalNumber0(xp) = all_12_0_10
% 220.99/171.25  																																																																																																																																																																																																																																																																																								| (3405) all_47_3_84 = all_12_0_10
% 220.99/171.25  																																																																																																																																																																																																																																																																																								|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| Combining equations (2191,3405) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (1281) all_12_0_10 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| Combining equations (1281,3405) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (2191) all_47_3_84 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| From (1281) and (2042) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (824), into two cases.
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|-Branch one:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| From (1282) and (2382) follows:
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.25  																																																																																																																																																																																																																																																																																										|
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| (1311) $false
% 220.99/171.25  																																																																																																																																																																																																																																																																																										|
% 220.99/171.25  																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|-Branch two:
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (2385) aNaturalNumber0(xm) = all_24_2_30
% 220.99/171.25  																																																																																																																																																																																																																																																																																									| (3413) all_24_2_30 = all_20_1_23
% 220.99/171.25  																																																																																																																																																																																																																																																																																									|
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| Combining equations (1282,3413) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| (1228) all_20_1_23 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																										|
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| Combining equations (1228,3413) yields a new equation:
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 220.99/171.25  																																																																																																																																																																																																																																																																																										|
% 220.99/171.25  																																																																																																																																																																																																																																																																																										| From (1282) and (2385) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																										|
% 220.99/171.26  																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (748), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																										|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																										| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 220.99/171.26  																																																																																																																																																																																																																																																																																										|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| From (1282) and (2382) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																										|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																										| (2385) aNaturalNumber0(xm) = all_24_2_30
% 220.99/171.26  																																																																																																																																																																																																																																																																																										| (3421) all_47_1_82 = all_24_2_30
% 220.99/171.26  																																																																																																																																																																																																																																																																																										|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| Combining equations (1237,3421) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| Combining equations (1282,3421) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (1237) all_47_1_82 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| From (1282) and (2385) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (409), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (3425)  ~ (aNaturalNumber0(xr) = all_16_0_16)
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| From (1931)(1292) and (3425) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| Using (1665) and (1670) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (3428) aNaturalNumber0(xr) = all_16_0_16
% 220.99/171.26  																																																																																																																																																																																																																																																																																											| (1292) all_16_0_16 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																											|
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| From (1931)(1292) and (3428) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|
% 220.99/171.26  																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (986), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| From (1294) and (1953) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| (1956) aNaturalNumber0(xn) = all_77_2_105
% 220.99/171.26  																																																																																																																																																																																																																																																																																												| (3435) all_77_2_105 = all_57_1_89
% 220.99/171.26  																																																																																																																																																																																																																																																																																												|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| Combining equations (1294,3435) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (980) all_57_1_89 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| Combining equations (980,3435) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| From (1294) and (1956) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (781), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| From (1294) and (2275) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (2278) aNaturalNumber0(xm) = all_77_2_105
% 220.99/171.26  																																																																																																																																																																																																																																																																																													| (3443) all_77_2_105 = all_37_3_64
% 220.99/171.26  																																																																																																																																																																																																																																																																																													|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| Combining equations (1294,3443) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (1233) all_37_3_64 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| Combining equations (1233,3443) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| From (1294) and (2278) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (793), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (3447)  ~ (aNaturalNumber0(sz10) = all_22_1_26)
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| From (1229) and (3447) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (3450) aNaturalNumber0(sz10) = all_22_1_26
% 220.99/171.26  																																																																																																																																																																																																																																																																																														| (1229) all_22_1_26 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																														|
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| From (1229) and (3450) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|
% 220.99/171.26  																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1019), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| From (1244) and (2604) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| (2607) aNaturalNumber0(xn) = all_72_1_100
% 220.99/171.26  																																																																																																																																																																																																																																																																																															| (3457) all_72_1_100 = all_39_8_74
% 220.99/171.26  																																																																																																																																																																																																																																																																																															|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| Combining equations (1244,3457) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (1179) all_39_8_74 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| Combining equations (1179,3457) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (1244) all_72_1_100 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| From (1244) and (2607) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (998), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| From (1233) and (3295) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (3298) aNaturalNumber0(xn) = all_37_3_64
% 220.99/171.26  																																																																																																																																																																																																																																																																																																| (3465) all_57_1_89 = all_37_3_64
% 220.99/171.26  																																																																																																																																																																																																																																																																																																|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| Combining equations (980,3465) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (1233) all_37_3_64 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| Combining equations (1233,3465) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (980) all_57_1_89 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| From (1233) and (3298) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (512), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (3469)  ~ (aNaturalNumber0(xk) = all_77_2_105)
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| From (1294) and (3469) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| Using (1665) and (1670) yields:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| (1311) $false
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|-Branch two:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (3472) aNaturalNumber0(xk) = all_77_2_105
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	| (3473) all_77_2_105 = all_52_2_87
% 220.99/171.26  																																																																																																																																																																																																																																																																																																	|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| Combining equations (1294,3473) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| (1674) all_52_2_87 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| Combining equations (1674,3473) yields a new equation:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| (1294) all_77_2_105 = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| From (1294) and (3472) follows:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| (1665) aNaturalNumber0(xk) = 0
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1016), into two cases.
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		|-Branch one:
% 220.99/171.26  																																																																																																																																																																																																																																																																																																		| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| From (1282) and (2210) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																		|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																		| (2213) aNaturalNumber0(xn) = all_24_2_30
% 220.99/171.27  																																																																																																																																																																																																																																																																																																		| (3481) all_39_8_74 = all_24_2_30
% 220.99/171.27  																																																																																																																																																																																																																																																																																																		|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| Combining equations (1179,3481) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (1282) all_24_2_30 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| Combining equations (1282,3481) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (1179) all_39_8_74 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| From (1282) and (2213) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (764), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| From (1292) and (3485) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (3488) aNaturalNumber0(xm) = all_16_0_16
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			| (3489) all_39_7_73 = all_16_0_16
% 220.99/171.27  																																																																																																																																																																																																																																																																																																			|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| Combining equations (1236,3489) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| Combining equations (1292,3489) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (1236) all_39_7_73 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| From (1292) and (3488) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1023), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| From (1233) and (3295) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (3298) aNaturalNumber0(xn) = all_37_3_64
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				| (3497) all_39_8_74 = all_37_3_64
% 220.99/171.27  																																																																																																																																																																																																																																																																																																				|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| Combining equations (1179,3497) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (1233) all_37_3_64 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| From (1233) and (3298) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (733), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| From (1237) and (2490) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (2493) aNaturalNumber0(xn) = all_47_1_82
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					| (1237) all_47_1_82 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																					|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| From (1237) and (2493) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1062), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| From (1350) and (1985) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| (1988) aNaturalNumber0(xn) = all_24_0_28
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						| (3510) all_24_0_28 = all_18_2_21
% 220.99/171.27  																																																																																																																																																																																																																																																																																																						|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| Combining equations (1350,3510) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (1226) all_18_2_21 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| Combining equations (1226,3510) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| From (1350) and (1988) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (719), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| From (1791) and (1977) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (1980) aNaturalNumber0(xm) = all_72_2_101
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							| (3518) all_72_2_101 = all_67_1_96
% 220.99/171.27  																																																																																																																																																																																																																																																																																																							|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| Combining equations (1791,3518) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (1242) all_67_1_96 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| Combining equations (1242,3518) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (1791) all_72_2_101 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| From (1791) and (1980) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1055), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (3522)  ~ (aNaturalNumber0(sz10) = all_18_2_21)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| From (1226) and (3522) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| Using (61) and (1994) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (3525) aNaturalNumber0(sz10) = all_18_2_21
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								| (1226) all_18_2_21 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																								|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| From (1226) and (3525) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| (61) aNaturalNumber0(sz10) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (427), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| From (1350) and (2136) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| (2139) aNaturalNumber0(xm) = all_24_0_28
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									| (1350) all_24_0_28 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																									|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| From (1350) and (2139) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1067), into two cases.
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|-Branch one:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| From (1244) and (2604) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| (1311) $false
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|-Branch two:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| (2607) aNaturalNumber0(xn) = all_72_1_100
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										| (3538) all_72_1_100 = all_18_2_21
% 220.99/171.27  																																																																																																																																																																																																																																																																																																										|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| Combining equations (1244,3538) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| (1226) all_18_2_21 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| Combining equations (1226,3538) yields a new equation:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| (1244) all_72_1_100 = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| From (1244) and (2607) follows:
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 220.99/171.27  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1130), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											| (3542)  ~ (aNaturalNumber0(sz00) = all_12_2_12)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| From (1223) and (3542) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| Using (26) and (2070) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											| (3545) aNaturalNumber0(sz00) = all_12_2_12
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											| (1223) all_12_2_12 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																											|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| From (1223) and (3545) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| (26) aNaturalNumber0(sz00) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1044), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| From (1242) and (2334) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| (2337) aNaturalNumber0(xn) = all_67_1_96
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												| (3552) all_67_1_96 = all_37_4_65
% 220.99/171.28  																																																																																																																																																																																																																																																																																																												|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| Combining equations (1242,3552) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (1232) all_37_4_65 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| Combining equations (1232,3552) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (1242) all_67_1_96 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| From (1242) and (2337) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (731), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| From (1674) and (3035) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (3038) aNaturalNumber0(xm) = all_52_2_87
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													| (3560) all_67_1_96 = all_52_2_87
% 220.99/171.28  																																																																																																																																																																																																																																																																																																													|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| Combining equations (1242,3560) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (1674) all_52_2_87 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| From (1674) and (3038) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (947), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| From (1236) and (2522) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (2525) aNaturalNumber0(xn) = all_39_7_73
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														| (3567) all_77_1_104 = all_39_7_73
% 220.99/171.28  																																																																																																																																																																																																																																																																																																														|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| Combining equations (1246,3567) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (1236) all_39_7_73 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| Combining equations (1236,3567) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (1246) all_77_1_104 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| From (1236) and (2525) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (379), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (3571)  ~ (aNaturalNumber0(xr) = all_77_2_105)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| From (1931)(1294) and (3571) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| Using (1665) and (1670) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (3574) aNaturalNumber0(xr) = all_77_2_105
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															| (1294) all_77_2_105 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																															|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| From (1931)(1294) and (3574) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| (1665) aNaturalNumber0(xk) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (945), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| From (1244) and (2604) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| (2607) aNaturalNumber0(xn) = all_72_1_100
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																| (3581) all_77_1_104 = all_72_1_100
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| Combining equations (1246,3581) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (1244) all_72_1_100 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| Combining equations (1244,3581) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (1246) all_77_1_104 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| From (1244) and (2607) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (996), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| From (1237) and (2490) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (2493) aNaturalNumber0(xn) = all_47_1_82
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	| (3589) all_57_1_89 = all_47_1_82
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| Combining equations (980,3589) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (1237) all_47_1_82 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| Combining equations (1237,3589) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (980) all_57_1_89 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| From (1237) and (2493) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1052), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| From (1218) and (3165) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (3168) aNaturalNumber0(xn) = all_14_1_14
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		| (3597) all_37_4_65 = all_14_1_14
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| Combining equations (1232,3597) yields a new equation:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| (1218) all_14_1_14 = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| From (1218) and (3168) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (624), into two cases.
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				| From (1350) and (2899) follows:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.99/171.28  																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																			| (2902) aNaturalNumber0(xp) = all_24_0_28
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																			| (3604) all_47_3_84 = all_24_0_28
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| Combining equations (2191,3604) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| (1350) all_24_0_28 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| Combining equations (1350,3604) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| (2191) all_47_3_84 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| From (1350) and (2902) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1073), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| From (1227) and (1933) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| (1936) aNaturalNumber0(xn) = all_18_1_20
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				| (3612) all_18_1_20 = all_18_2_21
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| Combining equations (1227,3612) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (1226) all_18_2_21 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| Combining equations (1226,3612) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (1227) all_18_1_20 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| From (1227) and (1936) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (655), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| From (1292) and (2023) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (2026) aNaturalNumber0(xp) = all_16_0_16
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					| (3620) all_37_2_63 = all_16_0_16
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| Combining equations (1195,3620) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (1292) all_16_0_16 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| From (1292) and (2026) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (724), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| From (1294) and (2275) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (2278) aNaturalNumber0(xm) = all_77_2_105
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						| (3627) all_77_2_105 = all_67_1_96
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,3627) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (1242) all_67_1_96 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| Combining equations (1242,3627) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| From (1294) and (2278) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (625), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| From (1283) and (2007) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (2010) aNaturalNumber0(xp) = all_26_2_33
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							| (3635) all_47_3_84 = all_26_2_33
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| Combining equations (2191,3635) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (1283) all_26_2_33 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| From (1283) and (2010) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1135), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| From (1293) and (2061) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (2064) aNaturalNumber0(xn) = all_47_2_83
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								| (3642) all_47_2_83 = all_12_2_12
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| Combining equations (1293,3642) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (1223) all_12_2_12 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| Combining equations (1223,3642) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (1293) all_47_2_83 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| From (1293) and (2064) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (792), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| From (1229) and (2891) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (2894) aNaturalNumber0(xn) = all_22_1_26
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									| (1229) all_22_1_26 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| From (1229) and (2894) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1110), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| From (1293) and (2061) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| (2064) aNaturalNumber0(xn) = all_47_2_83
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										| (3656) all_47_2_83 = all_14_2_15
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| Combining equations (1293,3656) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (1200) all_14_2_15 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| Combining equations (1200,3656) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (1293) all_47_2_83 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| From (1293) and (2064) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1036), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| From (1293) and (2061) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (2064) aNaturalNumber0(xn) = all_47_2_83
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											| (3664) all_47_2_83 = all_37_4_65
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																											|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| Combining equations (1293,3664) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (1232) all_37_4_65 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| Combining equations (1232,3664) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (1293) all_47_2_83 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| From (1293) and (2064) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (705), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| From (1294) and (2275) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (2278) aNaturalNumber0(xm) = all_77_2_105
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												| (3672) all_77_2_105 = all_72_1_100
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																												|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| Combining equations (1294,3672) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| (1244) all_72_1_100 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| Combining equations (1244,3672) yields a new equation:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| From (1294) and (2278) follows:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1065), into two cases.
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.29  																																																																																																																																																																																																																																																																																																																														| From (1281) and (2374) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																													| (2377) aNaturalNumber0(xn) = all_12_0_10
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																													| (3680) all_18_2_21 = all_12_0_10
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																													|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| Combining equations (1226,3680) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| Combining equations (1281,3680) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (1226) all_18_2_21 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| From (1281) and (2377) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (713), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| From (1242) and (2334) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (2337) aNaturalNumber0(xn) = all_67_1_96
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														| (1242) all_67_1_96 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																														|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| From (1242) and (2337) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (953), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| From (1218) and (3165) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| (3168) aNaturalNumber0(xn) = all_14_1_14
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															| (3694) all_77_1_104 = all_14_1_14
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																															|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| Combining equations (1246,3694) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (1218) all_14_1_14 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| Combining equations (1218,3694) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (1246) all_77_1_104 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| From (1218) and (3168) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1095), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| From (1236) and (2522) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (2525) aNaturalNumber0(xn) = all_39_7_73
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																| (3702) all_39_7_73 = all_16_2_18
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| Combining equations (1236,3702) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (1225) all_16_2_18 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| Combining equations (1225,3702) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (1236) all_39_7_73 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| From (1236) and (2525) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (726), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| From (1292) and (3485) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (3488) aNaturalNumber0(xm) = all_16_0_16
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	| (3710) all_67_1_96 = all_16_0_16
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																	|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| Combining equations (1242,3710) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| Combining equations (1292,3710) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (1242) all_67_1_96 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| From (1292) and (3488) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1049), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| From (1228) and (2055) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (2058) aNaturalNumber0(xn) = all_20_1_23
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		| (3718) all_37_4_65 = all_20_1_23
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																		|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| Combining equations (1232,3718) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (1228) all_20_1_23 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| From (1228) and (2058) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (806), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| From (1350) and (2136) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (2139) aNaturalNumber0(xm) = all_24_0_28
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			| (3725) all_24_0_28 = all_22_1_26
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																			|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| Combining equations (1350,3725) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (1229) all_22_1_26 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| Combining equations (1229,3725) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (1350) all_24_0_28 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| From (1350) and (2139) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (672), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2159) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (2162) aNaturalNumber0(xp) = all_47_2_83
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				| (3733) all_47_2_83 = all_26_1_32
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																				|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| Combining equations (1293,3733) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (1202) all_26_1_32 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| Combining equations (1202,3733) yields a new equation:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2162) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (772), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (3737)  ~ (aNaturalNumber0(sz00) = all_37_3_64)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| From (1233) and (3737) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| Using (26) and (2070) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (3740) aNaturalNumber0(sz00) = all_37_3_64
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					| (1233) all_37_3_64 = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																					|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| From (1233) and (3740) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| (26) aNaturalNumber0(sz00) = 0
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (695), into two cases.
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							| From (1244) and (2604) follows:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 220.99/171.30  																																																																																																																																																																																																																																																																																																																																						| (2607) aNaturalNumber0(xn) = all_72_1_100
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																						| (1244) all_72_1_100 = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																						|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							| From (1244) and (2607) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1121), into two cases.
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| From (1233) and (3295) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							| (3298) aNaturalNumber0(xn) = all_37_3_64
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							| (3753) all_37_3_64 = all_14_2_15
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																							|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| Combining equations (1233,3753) yields a new equation:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (1200) all_14_2_15 = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| Combining equations (1200,3753) yields a new equation:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (1233) all_37_3_64 = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| From (1233) and (3298) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1104), into two cases.
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (3757)  ~ (aNaturalNumber0(sz10) = all_14_2_15)
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| From (1200) and (3757) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| Using (61) and (1994) yields:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (3760) aNaturalNumber0(sz10) = all_14_2_15
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								| (1200) all_14_2_15 = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																								|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| From (1200) and (3760) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| (61) aNaturalNumber0(sz10) = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (399), into two cases.
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| (3763)  ~ (aNaturalNumber0(sz00) = all_47_2_83)
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										| From (1293) and (3763) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										| Using (26) and (2070) yields:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| (3766) aNaturalNumber0(sz00) = all_47_2_83
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									| (1293) all_47_2_83 = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																									|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										| From (1293) and (3766) follows:
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										| (26) aNaturalNumber0(sz00) = 0
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										|
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (771), into two cases.
% 220.99/171.31  																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																										| (3769)  ~ (aNaturalNumber0(sz10) = all_37_3_64)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																										|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| From (1233) and (3769) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| Using (61) and (1994) yields:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																										| (3772) aNaturalNumber0(sz10) = all_37_3_64
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																										| (1233) all_37_3_64 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																										|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| From (1233) and (3772) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| (61) aNaturalNumber0(sz10) = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (973), into two cases.
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| From (1233) and (3295) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| (3298) aNaturalNumber0(xn) = all_37_3_64
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											| (3779) all_62_1_93 = all_37_3_64
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																											|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| Combining equations (1240,3779) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (1233) all_37_3_64 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| Combining equations (1233,3779) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (1240) all_62_1_93 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| From (1233) and (3298) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (939), into two cases.
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| From (1292) and (2984) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (2987) aNaturalNumber0(xn) = all_16_0_16
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												| (3787) all_77_1_104 = all_16_0_16
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																												|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| Combining equations (1246,3787) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| Combining equations (1292,3787) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (1246) all_77_1_104 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| From (1292) and (2987) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (459), into two cases.
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (2089)  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| From (1292) and (2089) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| Using (1284) and (2090) yields:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (2092) aNaturalNumber0(all_0_9_9) = all_16_0_16
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													| (3795) all_26_2_33 = all_16_0_16
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																													|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| Combining equations (1283,3795) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (1292) all_16_0_16 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| Combining equations (1292,3795) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (1283) all_26_2_33 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| From (1292) and (2092) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (640), into two cases.
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| From (1292) and (2023) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (2026) aNaturalNumber0(xp) = all_16_0_16
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														| (3803) all_39_6_72 = all_16_0_16
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																														|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| Combining equations (629,3803) yields a new equation:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| (1292) all_16_0_16 = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| From (1292) and (2026) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (430), into two cases.
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															| (3806)  ~ (aNaturalNumber0(sz00) = all_24_0_28)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																															|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																																| From (1350) and (3806) follows:
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																																| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																																|
% 221.26/171.31  																																																																																																																																																																																																																																																																																																																																																| Using (26) and (2070) yields:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																															| (3809) aNaturalNumber0(sz00) = all_24_0_28
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																															| (1350) all_24_0_28 = 0
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																															|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																| From (1350) and (3809) follows:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																| (26) aNaturalNumber0(sz00) = 0
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (997), into two cases.
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| From (1236) and (2522) follows:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																| (2525) aNaturalNumber0(xn) = all_39_7_73
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																| (3816) all_57_1_89 = all_39_7_73
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| Combining equations (980,3816) yields a new equation:
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| (1236) all_39_7_73 = 0
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	|
% 221.26/171.32  																																																																																																																																																																																																																																																																																																																																																	| From (1236) and (2525) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (394), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	| (3819)  ~ (aNaturalNumber0(xr) = all_47_2_83)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| From (1931)(1293) and (3819) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| Using (1665) and (1670) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	| (3822) aNaturalNumber0(xr) = all_47_2_83
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| From (1931)(1293) and (3822) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| (1665) aNaturalNumber0(xk) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1043), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| From (1244) and (2604) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| (2607) aNaturalNumber0(xn) = all_72_1_100
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		| (3829) all_72_1_100 = all_37_4_65
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1244,3829) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (1232) all_37_4_65 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1232,3829) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (1244) all_72_1_100 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| From (1244) and (2607) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (609), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (2007) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (2010) aNaturalNumber0(xp) = all_26_2_33
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			| (3837) all_52_1_86 = all_26_2_33
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1238,3837) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1283,3837) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (1238) all_52_1_86 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (2010) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1134), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (1953) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (1956) aNaturalNumber0(xn) = all_77_2_105
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				| (3845) all_77_2_105 = all_12_2_12
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1294,3845) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (1223) all_12_2_12 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1223,3845) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (1956) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1102), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| From (1221) and (2081) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (2084) aNaturalNumber0(xn) = all_12_1_11
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					| (3853) all_16_2_18 = all_12_1_11
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| Combining equations (3853,1225) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (3284) all_12_1_11 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| Simplifying 3284 yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (1221) all_12_1_11 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| From (1221) and (2084) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (762), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (2275) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (2278) aNaturalNumber0(xm) = all_77_2_105
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						| (3861) all_77_2_105 = all_39_7_73
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,3861) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (1236) all_39_7_73 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1236,3861) yields a new equation:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (2278) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1056), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (3865)  ~ (aNaturalNumber0(sz00) = all_18_2_21)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| From (1226) and (3865) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| Using (26) and (2070) yields:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (3868) aNaturalNumber0(sz00) = all_18_2_21
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							| (1226) all_18_2_21 = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| From (1226) and (3868) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (903), into two cases.
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (2136) follows:
% 221.28/171.32  																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																								| (2139) aNaturalNumber0(xm) = all_24_0_28
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																								| (3875) all_24_0_28 = all_12_1_11
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1350,3875) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (1221) all_12_1_11 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1221,3875) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (1350) all_24_0_28 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (2139) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (927), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| From (1228) and (2055) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (2058) aNaturalNumber0(xn) = all_20_1_23
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									| (3883) all_82_1_108 = all_20_1_23
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1249,3883) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (1228) all_20_1_23 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1228,3883) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (1249) all_82_1_108 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| From (1228) and (2058) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (914), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| From (1293) and (2061) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (2064) aNaturalNumber0(xn) = all_47_2_83
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										| (3891) all_82_1_108 = all_47_2_83
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1249,3891) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (1293) all_47_2_83 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1293,3891) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (1249) all_82_1_108 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| From (1293) and (2064) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1088), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| From (1283) and (2252) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (2255) aNaturalNumber0(xn) = all_26_2_33
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											| (3899) all_26_2_33 = all_16_2_18
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1283,3899) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (1225) all_16_2_18 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1225,3899) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (1283) all_26_2_33 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| From (1283) and (2255) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (915), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| From (1292) and (2984) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (2987) aNaturalNumber0(xn) = all_16_0_16
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												| (3907) all_82_1_108 = all_16_0_16
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1249,3907) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1292,3907) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (1249) all_82_1_108 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| From (1292) and (2987) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (714), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (3911)  ~ (aNaturalNumber0(sz10) = all_67_1_96)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (3911) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| Using (61) and (1994) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (3914) aNaturalNumber0(sz10) = all_67_1_96
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													| (1242) all_67_1_96 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (3914) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| (61) aNaturalNumber0(sz10) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (687), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| From (1294) and (3339) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| (3342) aNaturalNumber0(xp) = all_77_2_105
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														| (3921) all_77_2_105 = all_24_1_29
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1294,3921) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (1207) all_24_1_29 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1207,3921) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (1294) all_77_2_105 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| From (1294) and (3342) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (770), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| From (1233) and (3295) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (3298) aNaturalNumber0(xn) = all_37_3_64
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															| (1233) all_37_3_64 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| From (1233) and (3298) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (688), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2159) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| (2162) aNaturalNumber0(xp) = all_47_2_83
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																| (3935) all_47_2_83 = all_24_1_29
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1293,3935) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| (1207) all_24_1_29 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1207,3935) yields a new equation:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2162) follows:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (866), into two cases.
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 221.28/171.33  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| From (1281) and (1969) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																	| (1972) aNaturalNumber0(xm) = all_12_0_10
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																	| (3943) all_16_1_17 = all_12_0_10
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (3943,848) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (2959) all_12_0_10 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| Simplifying 2959 yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| From (1281) and (1972) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (691), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (2007) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (2010) aNaturalNumber0(xp) = all_26_2_33
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		| (3951) all_26_2_33 = all_24_1_29
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,3951) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (1207) all_24_1_29 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1207,3951) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (2010) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (373), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (3955)  ~ (aNaturalNumber0(sz00) = all_20_2_24)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (3955) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| Using (26) and (2070) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (3958) aNaturalNumber0(sz00) = all_20_2_24
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (3958) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (917), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| From (1283) and (2252) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| (2255) aNaturalNumber0(xn) = all_26_2_33
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				| (3965) all_82_1_108 = all_26_2_33
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1249,3965) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (1283) all_26_2_33 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1283,3965) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (1249) all_82_1_108 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| From (1283) and (2255) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (384), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (3969)  ~ (aNaturalNumber0(sz00) = all_77_2_105)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (3969) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| Using (26) and (2070) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (3972) aNaturalNumber0(sz00) = all_77_2_105
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (3972) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (936), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2446) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| (2449) aNaturalNumber0(xn) = all_20_0_22
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						| (3979) all_77_1_104 = all_20_0_22
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1246,3979) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (1828) all_20_0_22 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1828,3979) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (1246) all_77_1_104 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2449) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (693), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| From (1281) and (2039) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (2042) aNaturalNumber0(xp) = all_12_0_10
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							| (3987) all_24_1_29 = all_12_0_10
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1207,3987) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (1281) all_12_0_10 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| From (1281) and (2042) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (482), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| From (1281) and (2039) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (2042) aNaturalNumber0(xp) = all_12_0_10
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								| (1281) all_12_0_10 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| From (1281) and (2042) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (729), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2382) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| (2385) aNaturalNumber0(xm) = all_24_2_30
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									| (4000) all_67_1_96 = all_24_2_30
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1242,4000) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1282,4000) yields a new equation:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (1242) all_67_1_96 = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2385) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (494), into two cases.
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (2312)  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2312) follows:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											| Using (1284) and (2090) yields:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.28/171.34  																																																																																																																																																																																																																																																																																																																																																																										| (2315) aNaturalNumber0(all_0_9_9) = all_22_2_27
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																										| (4008) all_22_2_27 = all_12_0_10
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (4008,1788) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| (2959) all_12_0_10 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| Simplifying 2959 yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| (1281) all_12_0_10 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2315) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (940), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| From (1350) and (1985) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| (1988) aNaturalNumber0(xn) = all_24_0_28
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											| (4016) all_77_1_104 = all_24_0_28
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1246,4016) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1350,4016) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (1246) all_77_1_104 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| From (1350) and (1988) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (751), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| From (1236) and (2522) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (2525) aNaturalNumber0(xn) = all_39_7_73
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												| (1236) all_39_7_73 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| From (1236) and (2525) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1020), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (2334) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| (2337) aNaturalNumber0(xn) = all_67_1_96
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													| (4030) all_67_1_96 = all_39_8_74
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1242,4030) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (1179) all_39_8_74 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1179,4030) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (1242) all_67_1_96 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (2337) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (363), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (4034)  ~ (aNaturalNumber0(sz00) = all_22_2_27)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (4034) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| Using (26) and (2070) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (4037) aNaturalNumber0(sz00) = all_22_2_27
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														| (1788) all_22_2_27 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (4037) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (930), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| From (1218) and (3165) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| (3168) aNaturalNumber0(xn) = all_14_1_14
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															| (4044) all_82_1_108 = all_14_1_14
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1249,4044) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (1218) all_14_1_14 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1218,4044) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (1249) all_82_1_108 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| From (1218) and (3168) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (667), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (2506) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (2509) aNaturalNumber0(xp) = all_62_2_94
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																| (4052) all_62_2_94 = all_26_1_32
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (4052,1790) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (4053) all_26_1_32 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| Simplifying 4053 yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (1202) all_26_1_32 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (2509) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (994), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| From (1244) and (2604) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (2607) aNaturalNumber0(xn) = all_72_1_100
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	| (4060) all_72_1_100 = all_57_1_89
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1244,4060) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (980) all_57_1_89 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (980,4060) yields a new equation:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (1244) all_72_1_100 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| From (1244) and (2607) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (325), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2298) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (2301) aNaturalNumber0(xm) = all_20_0_22
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2301) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (786), into two cases.
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																				| From (1282) and (2382) follows:
% 221.28/171.35  																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																			| (2385) aNaturalNumber0(xm) = all_24_2_30
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																			| (4074) all_37_3_64 = all_24_2_30
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1233,4074) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (1282) all_24_2_30 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1282,4074) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (1233) all_37_3_64 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| From (1282) and (2385) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1003), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| From (1218) and (3165) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (3168) aNaturalNumber0(xn) = all_14_1_14
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				| (4082) all_57_1_89 = all_14_1_14
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (980,4082) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (1218) all_14_1_14 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1218,4082) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (980) all_57_1_89 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| From (1218) and (3168) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (560), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2023) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (2026) aNaturalNumber0(xp) = all_16_0_16
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					| (4090) all_72_3_102 = all_16_0_16
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1243,4090) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (1292) all_16_0_16 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2026) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (614), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (2665) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (2668) aNaturalNumber0(xp) = all_67_2_97
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						| (4097) all_67_2_97 = all_47_3_84
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1829,4097) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (2191) all_47_3_84 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (2191,4097) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (2668) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (674), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (2899) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							| (4105) all_26_1_32 = all_24_0_28
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1202,4105) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (1350) all_24_0_28 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (2902) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1057), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2151) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (2154) aNaturalNumber0(xn) = all_82_2_109
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								| (4112) all_82_2_109 = all_18_2_21
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1830,4112) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (1226) all_18_2_21 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1226,4112) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2154) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1137), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (1985) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (1988) aNaturalNumber0(xn) = all_24_0_28
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									| (4120) all_24_0_28 = all_12_2_12
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1350,4120) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (1223) all_12_2_12 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1223,4120) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (1350) all_24_0_28 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (1988) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (755), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4124) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (4127) aNaturalNumber0(xm) = all_67_2_97
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										| (4128) all_67_2_97 = all_39_7_73
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,4128) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| (1236) all_39_7_73 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1236,4128) yields a new equation:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4127) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1041), into two cases.
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																												| From (1281) and (2374) follows:
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.36  																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																											| (2377) aNaturalNumber0(xn) = all_12_0_10
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																											| (4136) all_37_4_65 = all_12_0_10
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1232,4136) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| (1281) all_12_0_10 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| From (1281) and (2377) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (350), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| From (1789) and (2186) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| (2189) aNaturalNumber0(xp) = all_57_2_90
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| From (1789) and (2189) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (992), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (2374) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| (2377) aNaturalNumber0(xn) = all_12_0_10
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													| (4149) all_57_1_89 = all_12_0_10
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (980,4149) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (2377) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1105), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (4152)  ~ (aNaturalNumber0(sz00) = all_14_2_15)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| From (1200) and (4152) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| Using (26) and (2070) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (4155) aNaturalNumber0(sz00) = all_14_2_15
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														| (1200) all_14_2_15 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| From (1200) and (4155) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1090), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (2374) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| (2377) aNaturalNumber0(xn) = all_12_0_10
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															| (4162) all_16_2_18 = all_12_0_10
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (4162,1225) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (2959) all_12_0_10 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 2959 yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (1281) all_12_0_10 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (2377) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (535), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2665) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (2668) aNaturalNumber0(xp) = all_67_2_97
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																| (4170) all_77_3_106 = all_67_2_97
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1245,4170) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,4170) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (1245) all_77_3_106 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2668) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (715), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (4174)  ~ (aNaturalNumber0(sz00) = all_67_1_96)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| From (1242) and (4174) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| Using (26) and (2070) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (4177) aNaturalNumber0(sz00) = all_67_1_96
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	| (1242) all_67_1_96 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| From (1242) and (4177) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (775), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2298) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| (2301) aNaturalNumber0(xm) = all_20_0_22
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		| (4184) all_37_3_64 = all_20_0_22
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1233,4184) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1828) all_20_0_22 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1828,4184) yields a new equation:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1233) all_37_3_64 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2301) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (354), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1775) and (1780) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			| (1789) all_57_2_90 = 0
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (520), into two cases.
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2665) follows:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				| (2668) aNaturalNumber0(xp) = all_67_2_97
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				| (4196) all_82_3_110 = all_67_2_97
% 221.28/171.37  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1247,4196) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,4196) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| (1247) all_82_3_110 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2668) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (410), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2023) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| (2026) aNaturalNumber0(xp) = all_16_0_16
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					| (1292) all_16_0_16 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2026) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (716), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2097) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| (2100) aNaturalNumber0(xm) = all_82_2_109
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						| (4210) all_82_2_109 = all_67_1_96
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1830,4210) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (1242) all_67_1_96 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1242,4210) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2100) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (381), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (2275) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (2278) aNaturalNumber0(xm) = all_77_2_105
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (2278) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (867), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| From (1674) and (3035) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| (3038) aNaturalNumber0(xm) = all_52_2_87
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								| (4224) all_52_2_87 = all_16_1_17
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| From (1674) and (3038) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (389), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| (4226)  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (4226) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1295) and (2129) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| (4229) aNaturalNumber0(all_0_7_7) = all_72_2_101
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									| (4230) all_77_2_105 = all_72_2_101
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1294,4230) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1791,4230) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (1294) all_77_2_105 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (4229) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (1295) aNaturalNumber0(all_0_7_7) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (856), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (1939) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (1942) aNaturalNumber0(xm) = all_62_2_94
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										| (4238) all_62_2_94 = all_16_1_17
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (4238,1790) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (4239) all_16_1_17 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| Simplifying 4239 yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (848) all_16_1_17 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (1942) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (440), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (4242)  ~ (aNaturalNumber0(all_0_8_8) = all_77_2_105)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (4242) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1351) and (2575) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (4245) aNaturalNumber0(all_0_8_8) = all_77_2_105
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											| (4246) all_77_2_105 = all_24_0_28
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1294,4246) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1350,4246) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (1294) all_77_2_105 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (4245) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (1351) aNaturalNumber0(all_0_8_8) = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (978), into two cases.
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| From (1218) and (3165) follows:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (3168) aNaturalNumber0(xn) = all_14_1_14
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												| (4254) all_62_1_93 = all_14_1_14
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1240,4254) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| (1218) all_14_1_14 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1218,4254) yields a new equation:
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| (1240) all_62_1_93 = 0
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.38  																																																																																																																																																																																																																																																																																																																																																																																																													| From (1218) and (3168) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (460), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (2232)  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (2232) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1284) and (2090) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (2235) aNaturalNumber0(all_0_9_9) = all_24_0_28
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (4262) all_26_2_33 = all_24_0_28
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1283,4262) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1350) all_24_0_28 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1350,4262) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1283) all_26_2_33 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (2235) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (377), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2498) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1775) and (1780) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (4270) all_20_0_22 = all_20_2_24
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1828,4270) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (1787) all_20_2_24 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1787,4270) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2501) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (463), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| From (1282) and (2382) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (2385) aNaturalNumber0(xm) = all_24_2_30
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															| (1282) all_24_2_30 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| From (1282) and (2385) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (984), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2120) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| (2123) aNaturalNumber0(xn) = all_67_2_97
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																| (4284) all_67_2_97 = all_57_1_89
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,4284) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (980) all_57_1_89 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (980,4284) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2123) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (870), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (4288)  ~ (aNaturalNumber0(sz00) = all_14_1_14)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1218) and (4288) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (26) and (2070) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (4291) aNaturalNumber0(sz00) = all_14_1_14
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	| (1218) all_14_1_14 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1218) and (4291) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1004), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1221) and (2081) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| (2084) aNaturalNumber0(xn) = all_12_1_11
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		| (4298) all_57_1_89 = all_12_1_11
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (980,4298) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1221) all_12_1_11 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1221,4298) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (980) all_57_1_89 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1221) and (2084) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (974), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1229) and (2891) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (2894) aNaturalNumber0(xn) = all_22_1_26
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			| (4306) all_62_1_93 = all_22_1_26
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1240,4306) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1229) all_22_1_26 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1229,4306) yields a new equation:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1240) all_62_1_93 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1229) and (2894) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (425), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (4310)  ~ (aNaturalNumber0(xr) = all_24_0_28)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1931)(1350) and (4310) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1665) and (1670) yields:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (4313) aNaturalNumber0(xr) = all_24_0_28
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1350) all_24_0_28 = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1931)(1350) and (4313) follows:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1665) aNaturalNumber0(xk) = 0
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (977), into two cases.
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.39  																																																																																																																																																																																																																																																																																																																																																																																																																						| From (848) and (2268) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (2271) aNaturalNumber0(xn) = all_16_1_17
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (4320) all_62_1_93 = all_16_1_17
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1240,4320) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (848) all_16_1_17 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (848,4320) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (1240) all_62_1_93 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| From (848) and (2271) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (383), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (4324)  ~ (aNaturalNumber0(sz10) = all_77_2_105)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (4324) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (61) and (1994) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (4327) aNaturalNumber0(sz10) = all_77_2_105
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (4327) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (61) aNaturalNumber0(sz10) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (585), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1791) and (2642) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (2645) aNaturalNumber0(xp) = all_72_2_101
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (4334) all_72_2_101 = all_57_3_91
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1791,4334) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (2199) all_57_3_91 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (2199,4334) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (1791) all_72_2_101 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1791) and (2645) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (942), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2210) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (2213) aNaturalNumber0(xn) = all_24_2_30
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (4342) all_77_1_104 = all_24_2_30
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1246,4342) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1282,4342) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (1246) all_77_1_104 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2213) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (616), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (2642) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (2645) aNaturalNumber0(xp) = all_72_2_101
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (4350) all_72_2_101 = all_47_3_84
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1791,4350) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (2191) all_47_3_84 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (2191,4350) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (2645) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (711), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1281) and (1969) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1972) aNaturalNumber0(xm) = all_12_0_10
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										| (4358) all_72_1_100 = all_12_0_10
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1244,4358) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1281) all_12_0_10 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1281,4358) yields a new equation:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1244) all_72_1_100 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1281) and (1972) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (799), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (1939) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1942) aNaturalNumber0(xm) = all_62_2_94
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											| (4366) all_62_2_94 = all_22_1_26
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (1942) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (735), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| (4368)  ~ (aNaturalNumber0(sz00) = all_47_1_82)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1237) and (4368) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (26) and (2070) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| (4371) aNaturalNumber0(sz00) = all_47_1_82
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1237) all_47_1_82 = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1237) and (4371) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| (26) aNaturalNumber0(sz00) = 0
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (326), into two cases.
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1828) and (2446) follows:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.28/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| (2449) aNaturalNumber0(xn) = all_20_0_22
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													| (1828) all_20_0_22 = 0
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1828) and (2449) follows:
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1094), into two cases.
% 221.50/171.40  																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1237) and (2490) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (2493) aNaturalNumber0(xn) = all_47_1_82
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (4384) all_47_1_82 = all_16_2_18
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1237,4384) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (1225) all_16_2_18 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1225,4384) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (1237) all_47_1_82 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1237) and (2493) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (634), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (2506) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (2509) aNaturalNumber0(xp) = all_62_2_94
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (4392) all_62_2_94 = all_39_6_72
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (4392,1790) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (4393) all_39_6_72 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 4393 yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (629) all_39_6_72 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (2509) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (803), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1294) and (2275) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (2278) aNaturalNumber0(xm) = all_77_2_105
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (4400) all_77_2_105 = all_22_1_26
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1294,4400) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1229) all_22_1_26 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1229,4400) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1294) all_77_2_105 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1294) and (2278) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (615), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2171) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2174) aNaturalNumber0(xp) = all_20_0_22
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4408) all_47_3_84 = all_20_0_22
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (2191,4408) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2174) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1042), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (2552) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2555) aNaturalNumber0(xn) = all_52_2_87
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4415) all_52_2_87 = all_37_4_65
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (4415,1674) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4416) all_37_4_65 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| Simplifying 4416 yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1232) all_37_4_65 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (2555) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (802), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2366) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2369) aNaturalNumber0(xm) = all_20_2_24
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4423) all_22_1_26 = all_20_2_24
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1229,4423) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1787) all_20_2_24 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2369) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (382), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (1953) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1956) aNaturalNumber0(xn) = all_77_2_105
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1294) all_77_2_105 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (1956) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (610), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2475) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2478) aNaturalNumber0(xp) = all_24_2_30
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4436) all_52_1_86 = all_24_2_30
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1238,4436) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1282) all_24_2_30 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1282,4436) yields a new equation:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1238) all_52_1_86 = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2478) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1144), into two cases.
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1237) and (2490) follows:
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.41  																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2493) aNaturalNumber0(xn) = all_47_1_82
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4444) all_47_1_82 = all_12_2_12
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1237,4444) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1223) all_12_2_12 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1223,4444) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1237) all_47_1_82 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1237) and (2493) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (956), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4448)  ~ (aNaturalNumber0(sz10) = all_62_1_93)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1240) and (4448) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (61) and (1994) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4451) aNaturalNumber0(sz10) = all_62_1_93
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1240) all_62_1_93 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1240) and (4451) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (61) aNaturalNumber0(sz10) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1071), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1233) and (3295) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3298) aNaturalNumber0(xn) = all_37_3_64
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4458) all_37_3_64 = all_18_2_21
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1233,4458) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1226) all_18_2_21 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1226,4458) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1233) all_37_3_64 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1233) and (3298) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (456), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2218)  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1787) and (2218) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1284) and (2090) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2221) aNaturalNumber0(all_0_9_9) = all_20_2_24
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4466) all_26_2_33 = all_20_2_24
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1283,4466) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1787) all_20_2_24 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1787,4466) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1283) all_26_2_33 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1787) and (2221) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (745), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1293) and (2962) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2965) aNaturalNumber0(xm) = all_47_2_83
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4474) all_47_1_82 = all_47_2_83
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1237,4474) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1293) all_47_2_83 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1293,4474) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1237) all_47_1_82 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1293) and (2965) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (315), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4478)  ~ (aNaturalNumber0(xr) = all_67_2_97)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1931)(1829) and (4478) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1665) and (1670) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4481) aNaturalNumber0(xr) = all_67_2_97
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1931)(1829) and (4481) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1014), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (1985) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1988) aNaturalNumber0(xn) = all_24_0_28
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4488) all_39_8_74 = all_24_0_28
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1179,4488) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1350) all_24_0_28 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1350,4488) yields a new equation:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1179) all_39_8_74 = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (1988) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (372), into two cases.
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4492)  ~ (aNaturalNumber0(sz10) = all_20_2_24)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1787) and (4492) follows:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (61) and (1994) yields:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.50/171.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4495) aNaturalNumber0(sz10) = all_20_2_24
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1787) all_20_2_24 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1787) and (4495) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (61) aNaturalNumber0(sz10) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (364), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1775) and (1780) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1788) all_22_2_27 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (507), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4502)  ~ (aNaturalNumber0(xk) = all_72_2_101)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1791) and (4502) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1665) and (1670) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4505) aNaturalNumber0(xk) = all_72_2_101
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4506) all_72_2_101 = all_52_2_87
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1791,4506) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1674) all_52_2_87 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1674,4506) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1791) all_72_2_101 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1791) and (4505) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1665) aNaturalNumber0(xk) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (854), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2298) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2301) aNaturalNumber0(xm) = all_20_0_22
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4514) all_20_0_22 = all_16_1_17
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1828,4514) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (848) all_16_1_17 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (848,4514) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1828) all_20_0_22 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2301) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (868), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1218) and (3165) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3168) aNaturalNumber0(xn) = all_14_1_14
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1218) all_14_1_14 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1218) and (3168) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (680), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (2665) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2668) aNaturalNumber0(xp) = all_67_2_97
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4528) all_67_2_97 = all_24_1_29
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1829,4528) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1207) all_24_1_29 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1207,4528) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1829) all_67_2_97 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (2668) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (747), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (3028) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3031) aNaturalNumber0(xm) = all_26_2_33
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4536) all_47_1_82 = all_26_2_33
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1237,4536) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1283,4536) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1237) all_47_1_82 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (3031) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (835), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1790) and (1939) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1942) aNaturalNumber0(xm) = all_62_2_94
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4544) all_62_2_94 = all_18_1_20
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (4544,1790) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4545) all_18_1_20 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Simplifying 4545 yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1227) all_18_1_20 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1790) and (1942) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (402), into two cases.
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4548)  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (4548) follows:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1295) and (2129) yields:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4551) aNaturalNumber0(all_0_7_7) = all_67_2_97
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4552) all_67_2_97 = all_47_2_83
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,4552) yields a new equation:
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1293) all_47_2_83 = 0
% 221.50/171.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1293,4552) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (4551) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1295) aNaturalNumber0(all_0_7_7) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (663), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2112) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2115) aNaturalNumber0(xp) = all_82_2_109
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4560) all_82_2_109 = all_26_1_32
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1830,4560) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1202) all_26_1_32 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1202,4560) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2115) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (536), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2171) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2174) aNaturalNumber0(xp) = all_20_0_22
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4568) all_77_3_106 = all_20_0_22
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1245,4568) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1828) all_20_0_22 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1828,4568) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1245) all_77_3_106 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2174) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1131), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2151) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2154) aNaturalNumber0(xn) = all_82_2_109
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4576) all_82_2_109 = all_12_2_12
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1830,4576) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1223) all_12_2_12 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1223,4576) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2154) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (982), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4580)  ~ (aNaturalNumber0(sz00) = all_57_1_89)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (980) and (4580) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (26) and (2070) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4583) aNaturalNumber0(sz00) = all_57_1_89
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (980) all_57_1_89 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (980) and (4583) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (26) aNaturalNumber0(sz00) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (370), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2031) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2034) aNaturalNumber0(xp) = all_20_2_24
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1787) all_20_2_24 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2034) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1084), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (1953) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1956) aNaturalNumber0(xn) = all_77_2_105
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4596) all_77_2_105 = all_16_2_18
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1294,4596) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1225) all_16_2_18 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1225,4596) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1294) all_77_2_105 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (1956) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (758), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1790) and (1939) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1942) aNaturalNumber0(xm) = all_62_2_94
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4604) all_62_2_94 = all_39_7_73
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (4604,1790) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4605) all_39_7_73 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Simplifying 4605 yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1236) all_39_7_73 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1790) and (1942) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1001), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1227) and (1933) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1936) aNaturalNumber0(xn) = all_18_1_20
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4612) all_57_1_89 = all_18_1_20
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (980,4612) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1227) all_18_1_20 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1227,4612) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (980) all_57_1_89 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1227) and (1936) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (568), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2171) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2174) aNaturalNumber0(xp) = all_20_0_22
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4620) all_67_3_98 = all_20_0_22
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1241,4620) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1828,4620) yields a new equation:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1241) all_67_3_98 = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2174) follows:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (787), into two cases.
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.50/171.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (1969) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1972) aNaturalNumber0(xm) = all_12_0_10
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4628) all_37_3_64 = all_12_0_10
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1233,4628) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1281) all_12_0_10 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (1972) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1132), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2120) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2123) aNaturalNumber0(xn) = all_67_2_97
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4635) all_67_2_97 = all_12_2_12
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,4635) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1223) all_12_2_12 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1223,4635) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2123) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (698), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (4124) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4127) aNaturalNumber0(xm) = all_67_2_97
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4643) all_72_1_100 = all_67_2_97
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1244,4643) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,4643) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1244) all_72_1_100 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (4127) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (807), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (3028) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3031) aNaturalNumber0(xm) = all_26_2_33
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4651) all_26_2_33 = all_22_1_26
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,4651) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1229) all_22_1_26 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1229,4651) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (3031) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (912), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2446) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2449) aNaturalNumber0(xn) = all_20_0_22
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4659) all_82_1_108 = all_20_0_22
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1249,4659) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1828) all_20_0_22 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1828,4659) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1249) all_82_1_108 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2449) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (670), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1787) and (2031) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2034) aNaturalNumber0(xp) = all_20_2_24
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4667) all_26_1_32 = all_20_2_24
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1202,4667) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1787) all_20_2_24 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1787) and (2034) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (543), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1293) and (2159) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2162) aNaturalNumber0(xp) = all_47_2_83
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4674) all_77_3_106 = all_47_2_83
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1245,4674) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1293) all_47_2_83 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1293) and (2162) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (777), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1790) and (1939) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1942) aNaturalNumber0(xm) = all_62_2_94
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4681) all_62_2_94 = all_37_3_64
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (4681,1790) yields a new equation:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3040) all_37_3_64 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Simplifying 3040 yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1233) all_37_3_64 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1790) and (1942) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (466), into two cases.
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4685)  ~ (aNaturalNumber0(sz00) = all_24_2_30)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1282) and (4685) follows:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (26) and (2070) yields:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4688) aNaturalNumber0(sz00) = all_24_2_30
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1282) all_24_2_30 = 0
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1282) and (4688) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (898), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2144) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2147) aNaturalNumber0(xm) = all_22_2_27
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4695) all_22_2_27 = all_12_1_11
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (4695,1788) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3284) all_12_1_11 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Simplifying 3284 yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1221) all_12_1_11 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2147) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (706), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1293) and (2962) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2965) aNaturalNumber0(xm) = all_47_2_83
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4703) all_72_1_100 = all_47_2_83
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1244,4703) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1293) all_47_2_83 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1293,4703) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1244) all_72_1_100 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1293) and (2965) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1026), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1227) and (1933) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1936) aNaturalNumber0(xn) = all_18_1_20
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4711) all_39_8_74 = all_18_1_20
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1179,4711) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1227) all_18_1_20 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1227) and (1936) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (525), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2105) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2108) aNaturalNumber0(xp) = all_22_2_27
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4718) all_82_3_110 = all_22_2_27
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1247,4718) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1788,4718) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1247) all_82_3_110 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2108) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1070), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1236) and (2522) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2525) aNaturalNumber0(xn) = all_39_7_73
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4726) all_39_7_73 = all_18_2_21
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1236,4726) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1226) all_18_2_21 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1226,4726) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1236) all_39_7_73 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1236) and (2525) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (553), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (2642) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2645) aNaturalNumber0(xp) = all_72_2_101
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4734) all_72_2_101 = all_72_3_102
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1791,4734) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1243) all_72_3_102 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1243,4734) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1791) all_72_2_101 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (2645) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (679), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2112) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2115) aNaturalNumber0(xp) = all_82_2_109
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4742) all_82_2_109 = all_24_1_29
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1830,4742) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1207) all_24_1_29 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1207,4742) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2115) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (738), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2298) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2301) aNaturalNumber0(xm) = all_20_0_22
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4750) all_47_1_82 = all_20_0_22
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1237,4750) yields a new equation:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1828) all_20_0_22 = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2301) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (586), into two cases.
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (2506) follows:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.50/171.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2509) aNaturalNumber0(xp) = all_62_2_94
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4757) all_62_2_94 = all_57_3_91
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (2509) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (951), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1227) and (1933) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1936) aNaturalNumber0(xn) = all_18_1_20
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4763) all_77_1_104 = all_18_1_20
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1246,4763) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1227) all_18_1_20 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1227,4763) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1246) all_77_1_104 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1227) and (1936) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (833), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2298) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2301) aNaturalNumber0(xm) = all_20_0_22
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4771) all_20_0_22 = all_18_1_20
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1828,4771) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1227) all_18_1_20 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1227,4771) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1828) all_20_0_22 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2301) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (637), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2031) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2034) aNaturalNumber0(xp) = all_20_2_24
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4779) all_39_6_72 = all_20_2_24
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (629,4779) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1787) all_20_2_24 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2034) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (911), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2120) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2123) aNaturalNumber0(xn) = all_67_2_97
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4786) all_82_1_108 = all_67_2_97
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1249,4786) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,4786) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1249) all_82_1_108 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2123) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1000), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1228) and (2055) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2058) aNaturalNumber0(xn) = all_20_1_23
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4794) all_57_1_89 = all_20_1_23
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (980,4794) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1228) all_20_1_23 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1228) and (2058) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (542), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3339) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3342) aNaturalNumber0(xp) = all_77_2_105
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4801) all_77_2_105 = all_77_3_106
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,4801) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1245) all_77_3_106 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1245,4801) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3342) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (635), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1789) and (2186) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2189) aNaturalNumber0(xp) = all_57_2_90
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4809) all_57_2_90 = all_39_6_72
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1789,4809) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (629) all_39_6_72 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (629,4809) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1789) all_57_2_90 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1789) and (2189) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (728), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1283) and (3028) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3031) aNaturalNumber0(xm) = all_26_2_33
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4817) all_67_1_96 = all_26_2_33
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1242,4817) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1283) all_26_2_33 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1283,4817) yields a new equation:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1242) all_67_1_96 = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1283) and (3031) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (492), into two cases.
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4821)  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1790) and (4821) follows:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1284) and (2090) yields:
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.50/171.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4824) aNaturalNumber0(all_0_9_9) = all_62_2_94
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4825) all_62_2_94 = all_12_0_10
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (4825,1790) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2959) all_12_0_10 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Simplifying 2959 yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1281) all_12_0_10 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1790) and (4824) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1089), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1282) and (2210) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2213) aNaturalNumber0(xn) = all_24_2_30
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4833) all_24_2_30 = all_16_2_18
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1282,4833) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1225) all_16_2_18 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1225,4833) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1282) and (2213) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1059), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2446) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2449) aNaturalNumber0(xn) = all_20_0_22
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4841) all_20_0_22 = all_18_2_21
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1828,4841) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1226) all_18_2_21 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1226,4841) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2449) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (995), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1242) and (2334) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2337) aNaturalNumber0(xn) = all_67_1_96
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4849) all_67_1_96 = all_57_1_89
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1242,4849) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (980) all_57_1_89 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (980,4849) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1242) all_67_1_96 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1242) and (2337) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (685), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1788) and (2105) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2108) aNaturalNumber0(xp) = all_22_2_27
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4857) all_24_1_29 = all_22_2_27
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1207,4857) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1788) all_22_2_27 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1788) and (2108) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (931), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1221) and (2081) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2084) aNaturalNumber0(xn) = all_12_1_11
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4864) all_82_1_108 = all_12_1_11
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1249,4864) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1221) all_12_1_11 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1221,4864) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1249) all_82_1_108 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1221) and (2084) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (701), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (1939) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1942) aNaturalNumber0(xm) = all_62_2_94
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4872) all_72_1_100 = all_62_2_94
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1244,4872) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1790) all_62_2_94 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1790,4872) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1244) all_72_1_100 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (1942) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1061), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (2984) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2987) aNaturalNumber0(xn) = all_16_0_16
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4880) all_18_2_21 = all_16_0_16
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1226,4880) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1292,4880) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1226) all_18_2_21 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (2987) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (723), into two cases.
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1787) and (2366) follows:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2369) aNaturalNumber0(xm) = all_20_2_24
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4888) all_67_1_96 = all_20_2_24
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1242,4888) yields a new equation:
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1787) all_20_2_24 = 0
% 221.50/171.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1787,4888) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1242) all_67_1_96 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1787) and (2369) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1051), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (848) and (2268) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2271) aNaturalNumber0(xn) = all_16_1_17
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4896) all_37_4_65 = all_16_1_17
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1232,4896) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (848) all_16_1_17 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (848,4896) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1232) all_37_4_65 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (848) and (2271) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (397), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2061) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2064) aNaturalNumber0(xn) = all_47_2_83
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2064) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (671), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (3339) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (3342) aNaturalNumber0(xp) = all_77_2_105
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4910) all_77_2_105 = all_26_1_32
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1294,4910) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1202) all_26_1_32 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1202,4910) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (3342) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (737), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (4124) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4127) aNaturalNumber0(xm) = all_67_2_97
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4918) all_67_2_97 = all_47_1_82
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,4918) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1237) all_47_1_82 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1237,4918) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (4127) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (967), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (2374) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2377) aNaturalNumber0(xn) = all_12_0_10
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4926) all_62_1_93 = all_12_0_10
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1240,4926) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1281) all_12_0_10 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1281,4926) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1240) all_62_1_93 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (2377) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (561), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (2899) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4934) all_72_3_102 = all_24_0_28
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1243,4934) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1350) all_24_0_28 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1350,4934) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1243) all_72_3_102 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (2902) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (909), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4938)  ~ (aNaturalNumber0(sz00) = all_82_1_108)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1249) and (4938) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (26) and (2070) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4941) aNaturalNumber0(sz00) = all_82_1_108
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1249) all_82_1_108 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1249) and (4941) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (26) aNaturalNumber0(sz00) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (664), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1829) and (2665) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2668) aNaturalNumber0(xp) = all_67_2_97
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4948) all_67_2_97 = all_26_1_32
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1829,4948) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1202) all_26_1_32 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1202,4948) yields a new equation:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1829) all_67_2_97 = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1829) and (2668) follows:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (913), into two cases.
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (1953) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1956) aNaturalNumber0(xn) = all_77_2_105
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4956) all_82_1_108 = all_77_2_105
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1249,4956) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,4956) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1249) all_82_1_108 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (1956) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (357), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2498) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1775) and (1780) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4964) all_57_2_90 = all_20_0_22
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1789,4964) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1828,4964) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2501) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (921), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1244) and (2604) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2607) aNaturalNumber0(xn) = all_72_1_100
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4972) all_82_1_108 = all_72_1_100
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1249,4972) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1244) all_72_1_100 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1244,4972) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1249) all_82_1_108 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1244) and (2607) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (522), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (2642) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2645) aNaturalNumber0(xp) = all_72_2_101
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4980) all_82_3_110 = all_72_2_101
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1247,4980) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1791) all_72_2_101 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (2645) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (690), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2899) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4987) all_24_0_28 = all_24_1_29
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1350,4987) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1207) all_24_1_29 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1207,4987) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1350) all_24_0_28 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2902) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (926), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1229) and (2891) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2894) aNaturalNumber0(xn) = all_22_1_26
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4995) all_82_1_108 = all_22_1_26
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1249,4995) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1229) all_22_1_26 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1229,4995) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1249) all_82_1_108 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1229) and (2894) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (689), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (2023) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2026) aNaturalNumber0(xp) = all_16_0_16
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5003) all_24_1_29 = all_16_0_16
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1207,5003) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (2026) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (433), into two cases.
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5006)  ~ (aNaturalNumber0(all_0_8_8) = all_67_2_97)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (5006) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1351) and (2575) yields:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5009) aNaturalNumber0(all_0_8_8) = all_67_2_97
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5010) all_67_2_97 = all_24_0_28
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,5010) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1350,5010) yields a new equation:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (5009) follows:
% 221.65/171.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1351) aNaturalNumber0(all_0_8_8) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (916), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1350) and (1985) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1988) aNaturalNumber0(xn) = all_24_0_28
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5018) all_82_1_108 = all_24_0_28
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1249,5018) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1350) all_24_0_28 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1350,5018) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1249) all_82_1_108 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1350) and (1988) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (406), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5022)  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1789) and (5022) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1295) and (2129) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5025) aNaturalNumber0(all_0_7_7) = all_57_2_90
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5026) all_57_2_90 = all_47_2_83
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1789,5026) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,5026) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1789) all_57_2_90 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1789) and (5025) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1295) aNaturalNumber0(all_0_7_7) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (918), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1282) and (2210) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2213) aNaturalNumber0(xn) = all_24_2_30
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5034) all_82_1_108 = all_24_2_30
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1249,5034) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1282) all_24_2_30 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1282,5034) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1249) all_82_1_108 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1282) and (2213) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (613), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2112) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2115) aNaturalNumber0(xp) = all_82_2_109
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5042) all_82_2_109 = all_47_3_84
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1830,5042) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2191) all_47_3_84 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (2191,5042) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1830) all_82_2_109 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2115) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (438), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5046)  ~ (aNaturalNumber0(all_0_8_8) = all_22_2_27)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1788) and (5046) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (1351) and (2575) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5049) aNaturalNumber0(all_0_8_8) = all_22_2_27
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5050) all_24_0_28 = all_22_2_27
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1350,5050) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1788) all_22_2_27 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1788,5050) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1788) and (5049) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1351) aNaturalNumber0(all_0_8_8) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (642), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1283) and (2007) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2010) aNaturalNumber0(xp) = all_26_2_33
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5058) all_39_6_72 = all_26_2_33
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (629,5058) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1283) all_26_2_33 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1283,5058) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (629) all_39_6_72 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1283) and (2010) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (877), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2144) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2147) aNaturalNumber0(xm) = all_22_2_27
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5066) all_22_2_27 = all_14_1_14
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (5066,1788) yields a new equation:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1217) all_14_1_14 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Simplifying 1217 yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1218) all_14_1_14 = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2147) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (985), into two cases.
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1828) and (2446) follows:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.65/171.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2449) aNaturalNumber0(xn) = all_20_0_22
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5074) all_57_1_89 = all_20_0_22
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (980,5074) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1828) all_20_0_22 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1828,5074) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (980) all_57_1_89 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1828) and (2449) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (590), into two cases.
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (3339) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3342) aNaturalNumber0(xp) = all_77_2_105
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5082) all_77_2_105 = all_57_3_91
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,5082) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2199) all_57_3_91 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (2199,5082) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (3342) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (510), into two cases.
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5086)  ~ (aNaturalNumber0(xk) = all_22_2_27)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (5086) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1665) and (1670) yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5089) aNaturalNumber0(xk) = all_22_2_27
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5090) all_52_2_87 = all_22_2_27
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (5090,1674) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5091) all_22_2_27 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Simplifying 5091 yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (5089) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (517), into two cases.
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5094)  ~ (aNaturalNumber0(xk) = all_24_2_30)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (5094) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1665) and (1670) yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5097) aNaturalNumber0(xk) = all_24_2_30
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5098) all_52_2_87 = all_24_2_30
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (5098,1674) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5099) all_24_2_30 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Simplifying 5099 yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (5097) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1665) aNaturalNumber0(xk) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1096), into two cases.
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1233) and (3295) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3298) aNaturalNumber0(xn) = all_37_3_64
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5106) all_37_3_64 = all_16_2_18
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1233,5106) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1225) all_16_2_18 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1225,5106) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1233) all_37_3_64 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1233) and (3298) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (519), into two cases.
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2112) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2115) aNaturalNumber0(xp) = all_82_2_109
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5114) all_82_2_109 = all_82_3_110
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1830,5114) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1247) all_82_3_110 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1247,5114) yields a new equation:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2115) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (312), into two cases.
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5118)  ~ (aNaturalNumber0(sz10) = all_82_2_109)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (5118) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5121) aNaturalNumber0(sz10) = all_82_2_109
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (5121) follows:
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (465), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5124)  ~ (aNaturalNumber0(sz10) = all_24_2_30)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1282) and (5124) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (61) and (1994) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5127) aNaturalNumber0(sz10) = all_24_2_30
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1282) all_24_2_30 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1282) and (5127) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (61) aNaturalNumber0(sz10) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (445), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1283) and (2252) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2255) aNaturalNumber0(xn) = all_26_2_33
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1283) all_26_2_33 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1283) and (2255) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (595), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1282) and (2475) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2478) aNaturalNumber0(xp) = all_24_2_30
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5140) all_57_3_91 = all_24_2_30
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (2199,5140) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1282) all_24_2_30 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1282,5140) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2199) all_57_3_91 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1282) and (2478) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (636), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2105) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2108) aNaturalNumber0(xp) = all_22_2_27
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5148) all_39_6_72 = all_22_2_27
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (629,5148) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1788) all_22_2_27 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2108) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1050), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1227) and (1933) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1936) aNaturalNumber0(xn) = all_18_1_20
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5155) all_37_4_65 = all_18_1_20
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1232,5155) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1227) all_18_1_20 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1227) and (1936) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (675), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1283) and (2007) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2010) aNaturalNumber0(xp) = all_26_2_33
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5162) all_26_1_32 = all_26_2_33
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1202,5162) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1283) all_26_2_33 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1283) and (2010) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (506), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5165)  ~ (aNaturalNumber0(xk) = all_20_0_22)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (5165) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (1665) and (1670) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5168) aNaturalNumber0(xk) = all_20_0_22
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5169) all_52_2_87 = all_20_0_22
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (5169,1674) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2724) all_20_0_22 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Simplifying 2724 yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1828) all_20_0_22 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (5168) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1665) aNaturalNumber0(xk) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (352), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5173)  ~ (aNaturalNumber0(sz10) = all_57_2_90)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1789) and (5173) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (61) and (1994) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5176) aNaturalNumber0(sz10) = all_57_2_90
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1789) all_57_2_90 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1789) and (5176) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (61) aNaturalNumber0(sz10) = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (760), into two cases.
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2144) follows:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2147) aNaturalNumber0(xm) = all_22_2_27
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5183) all_39_7_73 = all_22_2_27
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1236,5183) yields a new equation:
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1788) all_22_2_27 = 0
% 221.65/171.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1788,5183) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1236) all_39_7_73 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2147) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (524), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (2186) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2189) aNaturalNumber0(xp) = all_57_2_90
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5191) all_82_3_110 = all_57_2_90
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1247,5191) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1789) all_57_2_90 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1789,5191) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1247) all_82_3_110 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (2189) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (798), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1791) and (1977) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1980) aNaturalNumber0(xm) = all_72_2_101
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5199) all_72_2_101 = all_22_1_26
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1791,5199) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1229) all_22_1_26 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1229,5199) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1791) all_72_2_101 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1791) and (1980) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1075), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1218) and (3165) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3168) aNaturalNumber0(xn) = all_14_1_14
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5207) all_18_2_21 = all_14_1_14
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1226,5207) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1218) all_14_1_14 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1218) and (3168) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (649), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1790) and (2506) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2509) aNaturalNumber0(xp) = all_62_2_94
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5214) all_62_2_94 = all_37_2_63
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1790) and (2509) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (471), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5216)  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (5216) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1284) and (2090) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5219) aNaturalNumber0(all_0_9_9) = all_72_2_101
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5220) all_72_2_101 = all_24_2_30
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1791,5220) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1282) all_24_2_30 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1282,5220) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1791) all_72_2_101 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (5219) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (865), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1282) and (2382) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2385) aNaturalNumber0(xm) = all_24_2_30
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5228) all_24_2_30 = all_16_1_17
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1282,5228) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (848) all_16_1_17 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (848,5228) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1282) all_24_2_30 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1282) and (2385) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (761), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1787) and (2366) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2369) aNaturalNumber0(xm) = all_20_2_24
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5236) all_39_7_73 = all_20_2_24
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1236,5236) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1787) all_20_2_24 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1787) and (2369) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (645), into two cases.
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2112) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2115) aNaturalNumber0(xp) = all_82_2_109
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5243) all_82_2_109 = all_37_2_63
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1830,5243) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1195) all_37_2_63 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1195,5243) yields a new equation:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1830) all_82_2_109 = 0
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2115) follows:
% 221.65/171.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (742), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1788) and (2144) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2147) aNaturalNumber0(xm) = all_22_2_27
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5251) all_47_1_82 = all_22_2_27
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1237,5251) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1788) all_22_2_27 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1788,5251) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1237) all_47_1_82 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1788) and (2147) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (573), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2031) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2034) aNaturalNumber0(xp) = all_20_2_24
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5259) all_67_3_98 = all_20_2_24
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1241,5259) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1787,5259) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1241) all_67_3_98 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2034) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (809), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (3035) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3038) aNaturalNumber0(xm) = all_52_2_87
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5267) all_52_2_87 = all_22_1_26
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (5267,1674) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5268) all_22_1_26 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Simplifying 5268 yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1229) all_22_1_26 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (3038) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (666), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1791) and (2642) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2645) aNaturalNumber0(xp) = all_72_2_101
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5275) all_72_2_101 = all_26_1_32
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1791,5275) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1202) all_26_1_32 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1202,5275) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1791) all_72_2_101 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1791) and (2645) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1122), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1229) and (2891) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2894) aNaturalNumber0(xn) = all_22_1_26
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5283) all_22_1_26 = all_14_2_15
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1229,5283) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1200) all_14_2_15 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1200,5283) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1229) all_22_1_26 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1229) and (2894) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1008), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2151) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2154) aNaturalNumber0(xn) = all_82_2_109
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5291) all_82_2_109 = all_39_8_74
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1830,5291) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1179) all_39_8_74 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1179,5291) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2154) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (834), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1791) and (1977) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1980) aNaturalNumber0(xm) = all_72_2_101
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5299) all_72_2_101 = all_18_1_20
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1791,5299) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1227) all_18_1_20 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1227,5299) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1791) all_72_2_101 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1791) and (1980) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (683), into two cases.
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1790) and (2506) follows:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2509) aNaturalNumber0(xp) = all_62_2_94
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5307) all_62_2_94 = all_24_1_29
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (5307,1790) yields a new equation:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5308) all_24_1_29 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Simplifying 5308 yields:
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1207) all_24_1_29 = 0
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1790) and (2509) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (795), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2097) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2100) aNaturalNumber0(xm) = all_82_2_109
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5315) all_82_2_109 = all_22_1_26
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,5315) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1229) all_22_1_26 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1229,5315) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2100) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1082), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (2120) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2123) aNaturalNumber0(xn) = all_67_2_97
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5323) all_67_2_97 = all_16_2_18
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,5323) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1225) all_16_2_18 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1225,5323) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (2123) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (657), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1283) and (2007) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2010) aNaturalNumber0(xp) = all_26_2_33
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5331) all_37_2_63 = all_26_2_33
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1195,5331) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1283) all_26_2_33 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1283,5331) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1195) all_37_2_63 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1283) and (2010) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (386), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3255)  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (3255) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1295) and (2129) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3258) aNaturalNumber0(all_0_7_7) = all_82_2_109
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5339) all_82_2_109 = all_77_2_105
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1830,5339) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1294,5339) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1830) all_82_2_109 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (3258) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1295) aNaturalNumber0(all_0_7_7) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (784), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (2136) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2139) aNaturalNumber0(xm) = all_24_0_28
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5347) all_37_3_64 = all_24_0_28
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1233,5347) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1350) all_24_0_28 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1350,5347) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1233) all_37_3_64 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (2139) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (584), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2171) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2174) aNaturalNumber0(xp) = all_20_0_22
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5355) all_57_3_91 = all_20_0_22
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (2199,5355) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1828,5355) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2199) all_57_3_91 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2174) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (656), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2899) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5363) all_37_2_63 = all_24_0_28
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1195,5363) yields a new equation:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1350) all_24_0_28 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2902) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (415), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1295) and (2129) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1295) aNaturalNumber0(all_0_7_7) = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1292) all_16_0_16 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (317), into two cases.
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (4124) follows:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4127) aNaturalNumber0(xm) = all_67_2_97
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.65/171.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (4127) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (486), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5376)  ~ (aNaturalNumber0(sz00) = all_12_0_10)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1281) and (5376) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (26) and (2070) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5379) aNaturalNumber0(sz00) = all_12_0_10
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1281) and (5379) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (26) aNaturalNumber0(sz00) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1032), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (2151) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2154) aNaturalNumber0(xn) = all_82_2_109
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5386) all_82_2_109 = all_37_4_65
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1830,5386) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1232) all_37_4_65 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1232,5386) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1830) all_82_2_109 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (2154) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (484), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1281) and (2374) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2377) aNaturalNumber0(xn) = all_12_0_10
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1281) all_12_0_10 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1281) and (2377) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1048), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1229) and (2891) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2894) aNaturalNumber0(xn) = all_22_1_26
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5400) all_37_4_65 = all_22_1_26
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1232,5400) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1229) all_22_1_26 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1229) and (2894) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (497), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2467)  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1293) and (2467) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (1284) and (2090) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2470) aNaturalNumber0(all_0_9_9) = all_47_2_83
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5407) all_47_2_83 = all_12_0_10
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1293,5407) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1281) all_12_0_10 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1281,5407) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1293) all_47_2_83 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1293) and (2470) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1045), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1237) and (2490) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2493) aNaturalNumber0(xn) = all_47_1_82
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5415) all_47_1_82 = all_37_4_65
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1237,5415) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1232) all_37_4_65 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1232,5415) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1237) all_47_1_82 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1237) and (2493) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (478), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2089)  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1292) and (2089) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1284) and (2090) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2092) aNaturalNumber0(all_0_9_9) = all_16_0_16
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5423) all_24_2_30 = all_16_0_16
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1282,5423) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1292) all_16_0_16 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1292) and (2092) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (843), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1283) and (3028) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3031) aNaturalNumber0(xm) = all_26_2_33
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5430) all_26_2_33 = all_18_1_20
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1283,5430) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1227) all_18_1_20 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1227,5430) yields a new equation:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1283) all_26_2_33 = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1283) and (3031) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (476), into two cases.
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2326)  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (2326) follows:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1284) and (2090) yields:
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.65/171.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2329) aNaturalNumber0(all_0_9_9) = all_77_2_105
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5438) all_77_2_105 = all_24_2_30
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,5438) yields a new equation:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1282,5438) yields a new equation:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (2329) follows:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1284) aNaturalNumber0(all_0_9_9) = 0
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (422), into two cases.
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2620)  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2620) follows:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1295) and (2129) yields:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2623) aNaturalNumber0(all_0_7_7) = all_22_2_27
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5446) all_22_2_27 = all_16_0_16
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (5446,1788) yields a new equation:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2760) all_16_0_16 = 0
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Simplifying 2760 yields:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1292) all_16_0_16 = 0
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2623) follows:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1295) aNaturalNumber0(all_0_7_7) = 0
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (577), into two cases.
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.65/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (2899) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5454) all_67_3_98 = all_24_0_28
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1241,5454) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1350) all_24_0_28 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (2902) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (709), into two cases.
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (3028) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3031) aNaturalNumber0(xm) = all_26_2_33
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5461) all_72_1_100 = all_26_2_33
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1244,5461) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1283) all_26_2_33 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (3031) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (346), into two cases.
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (5464) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1775) and (1780) yields:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5468) all_82_2_109 = all_62_2_94
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1830,5468) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1790) all_62_2_94 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1790,5468) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (5467) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (744), into two cases.
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1294) and (2275) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2278) aNaturalNumber0(xm) = all_77_2_105
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5476) all_77_2_105 = all_47_1_82
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1294,5476) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1237) all_47_1_82 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1237,5476) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1294) all_77_2_105 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1294) and (2278) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (338), into two cases.
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (5480) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1775) and (1780) yields:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5484) all_72_2_101 = all_67_2_97
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1791,5484) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,5484) yields a new equation:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1791) all_72_2_101 = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (5483) follows:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1101), into two cases.
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1218) and (3165) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3168) aNaturalNumber0(xn) = all_14_1_14
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5492) all_16_2_18 = all_14_1_14
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (5492,1225) yields a new equation:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1217) all_14_1_14 = 0
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Simplifying 1217 yields:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1218) all_14_1_14 = 0
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1218) and (3168) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (343), into two cases.
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5496)  ~ (aNaturalNumber0(sz10) = all_62_2_94)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1790) and (5496) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (61) and (1994) yields:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5499) aNaturalNumber0(sz10) = all_62_2_94
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1790) all_62_2_94 = 0
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1790) and (5499) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (61) aNaturalNumber0(sz10) = 0
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1141), into two cases.
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (2552) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2555) aNaturalNumber0(xn) = all_52_2_87
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5506) all_52_2_87 = all_12_2_12
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (2555) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (532), into two cases.
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1282) and (2475) follows:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2478) aNaturalNumber0(xp) = all_24_2_30
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5512) all_82_3_110 = all_24_2_30
% 221.93/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1247,5512) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1282) all_24_2_30 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1282,5512) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1247) all_82_3_110 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1282) and (2478) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1119), into two cases.
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1237) and (2490) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2493) aNaturalNumber0(xn) = all_47_1_82
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5520) all_47_1_82 = all_14_2_15
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1237,5520) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1200) all_14_2_15 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1200,5520) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1237) all_47_1_82 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1237) and (2493) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (530), into two cases.
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2899) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5528) all_82_3_110 = all_24_0_28
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1247,5528) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1350,5528) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1247) all_82_3_110 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2902) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (650), into two cases.
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1789) and (2186) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2189) aNaturalNumber0(xp) = all_57_2_90
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5536) all_57_2_90 = all_37_2_63
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1789,5536) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1195) all_37_2_63 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1195,5536) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1789) all_57_2_90 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1789) and (2189) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (547), into two cases.
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2475) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2478) aNaturalNumber0(xp) = all_24_2_30
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5544) all_77_3_106 = all_24_2_30
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1245,5544) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1282,5544) yields a new equation:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1245) all_77_3_106 = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2478) follows:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (754), into two cases.
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 221.96/171.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2097) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2100) aNaturalNumber0(xm) = all_82_2_109
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5552) all_82_2_109 = all_39_7_73
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,5552) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1236) all_39_7_73 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1236,5552) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2100) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (545), into two cases.
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1350) and (2899) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2902) aNaturalNumber0(xp) = all_24_0_28
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5560) all_77_3_106 = all_24_0_28
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1245,5560) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1350,5560) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1245) all_77_3_106 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1350) and (2902) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (375), into two cases.
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1830) and (5464) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1775) and (1780) yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5568) all_82_2_109 = all_20_2_24
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1830,5568) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1787) all_20_2_24 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1787,5568) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1830) all_82_2_109 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1830) and (5467) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (862), into two cases.
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1292) and (3485) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3488) aNaturalNumber0(xm) = all_16_0_16
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5576) all_16_0_16 = all_16_1_17
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1292,5576) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (848) all_16_1_17 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (848,5576) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1292) and (3488) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (511), into two cases.
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5580)  ~ (aNaturalNumber0(xk) = all_20_2_24)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1787) and (5580) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1665) and (1670) yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5583) aNaturalNumber0(xk) = all_20_2_24
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5584) all_52_2_87 = all_20_2_24
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (5584,1674) yields a new equation:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1786) all_20_2_24 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Simplifying 1786 yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1787) all_20_2_24 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1787) and (5583) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1665) aNaturalNumber0(xk) = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (850), into two cases.
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5588)  ~ (aNaturalNumber0(sz10) = all_16_1_17)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (848) and (5588) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5591) aNaturalNumber0(sz10) = all_16_1_17
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (848) all_16_1_17 = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (848) and (5591) follows:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (327), into two cases.
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 221.96/171.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5594)  ~ (aNaturalNumber0(sz10) = all_20_0_22)
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (5594) follows:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5597) aNaturalNumber0(sz10) = all_20_0_22
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (5597) follows:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1147), into two cases.
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1229) and (2891) follows:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2894) aNaturalNumber0(xn) = all_22_1_26
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5604) all_22_1_26 = all_12_2_12
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1229,5604) yields a new equation:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1223) all_12_2_12 = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1223,5604) yields a new equation:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1229) all_22_1_26 = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1229) and (2894) follows:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (987), into two cases.
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2061) follows:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2064) aNaturalNumber0(xn) = all_47_2_83
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5612) all_57_1_89 = all_47_2_83
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (980,5612) yields a new equation:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1293,5612) yields a new equation:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (980) all_57_1_89 = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2064) follows:
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 221.96/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (391), into two cases.
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5022)  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (5022) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1295) and (2129) yields:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5025) aNaturalNumber0(all_0_7_7) = all_57_2_90
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5620) all_77_2_105 = all_57_2_90
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1294,5620) yields a new equation:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1789) all_57_2_90 = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1789,5620) yields a new equation:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1294) all_77_2_105 = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (5025) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (763), into two cases.
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2962) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5628) all_47_2_83 = all_39_7_73
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,5628) yields a new equation:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1236) all_39_7_73 = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1236,5628) yields a new equation:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2965) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (376), into two cases.
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (5480) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1775) and (1780) yields:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5636) all_67_2_97 = all_20_2_24
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,5636) yields a new equation:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1787) all_20_2_24 = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1787,5636) yields a new equation:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (5483) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (631), into two cases.
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2665) follows:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2668) aNaturalNumber0(xp) = all_67_2_97
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5644) all_67_2_97 = all_39_6_72
% 222.05/171.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,5644) yields a new equation:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (629) all_39_6_72 = 0
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (629,5644) yields a new equation:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2668) follows:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (717), into two cases.
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (4124) follows:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.05/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5652) all_67_1_96 = all_67_2_97
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1242,5652) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1829,5652) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1242) all_67_1_96 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (4127) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1047), into two cases.
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1233) and (3295) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3298) aNaturalNumber0(xn) = all_37_3_64
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5660) all_37_3_64 = all_37_4_65
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1233,5660) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1232) all_37_4_65 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1232,5660) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1233) all_37_3_64 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1233) and (3298) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (452), into two cases.
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5216)  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (5216) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1284) and (2090) yields:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5219) aNaturalNumber0(all_0_9_9) = all_72_2_101
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5668) all_72_2_101 = all_26_2_33
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1791,5668) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1283) all_26_2_33 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1283,5668) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (5219) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (310), into two cases.
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2097) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2100) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (468), into two cases.
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2290)  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (2290) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1284) and (2090) yields:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2293) aNaturalNumber0(all_0_9_9) = all_82_2_109
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5682) all_82_2_109 = all_24_2_30
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1830,5682) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1282,5682) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1830) all_82_2_109 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (2293) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1118), into two cases.
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1242) and (2334) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2337) aNaturalNumber0(xn) = all_67_1_96
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5690) all_67_1_96 = all_14_2_15
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1242,5690) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1200) all_14_2_15 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1200,5690) yields a new equation:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1242) all_67_1_96 = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1242) and (2337) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (472), into two cases.
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4821)  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1790) and (4821) follows:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1284) and (2090) yields:
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.08/171.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4824) aNaturalNumber0(all_0_9_9) = all_62_2_94
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5698) all_62_2_94 = all_24_2_30
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (5698,1790) yields a new equation:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5099) all_24_2_30 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Simplifying 5099 yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1790) and (4824) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (533), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (2039) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2042) aNaturalNumber0(xp) = all_12_0_10
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5706) all_82_3_110 = all_12_0_10
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1247,5706) yields a new equation:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1281,5706) yields a new equation:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1247) all_82_3_110 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (2042) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (515), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5710)  ~ (aNaturalNumber0(xk) = all_24_0_28)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (5710) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1665) and (1670) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5713) aNaturalNumber0(xk) = all_24_0_28
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5714) all_52_2_87 = all_24_0_28
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (5714,1674) yields a new equation:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5715) all_24_0_28 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Simplifying 5715 yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1350) all_24_0_28 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (5713) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1665) aNaturalNumber0(xk) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (485), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5718)  ~ (aNaturalNumber0(sz10) = all_12_0_10)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (5718) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5721) aNaturalNumber0(sz10) = all_12_0_10
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (5721) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (448), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1284) and (2090) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1283) all_26_2_33 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (873), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2298) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2301) aNaturalNumber0(xm) = all_20_0_22
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5732) all_20_0_22 = all_14_1_14
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1828,5732) yields a new equation:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1218) all_14_1_14 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1218,5732) yields a new equation:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2301) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (398), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5736)  ~ (aNaturalNumber0(sz10) = all_47_2_83)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (5736) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (61) and (1994) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5739) aNaturalNumber0(sz10) = all_47_2_83
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (5739) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (61) aNaturalNumber0(sz10) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (371), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2366) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2369) follows:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (652), into two cases.
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1787) and (2031) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5752) all_37_2_63 = all_20_2_24
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1195,5752) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1787) all_20_2_24 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1787) and (2034) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (831), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2097) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5759) all_82_2_109 = all_18_1_20
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1830,5759) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1227) all_18_1_20 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1227,5759) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1830) all_82_2_109 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2100) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (697), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2097) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5767) all_82_2_109 = all_72_1_100
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1830,5767) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1244) all_72_1_100 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1244,5767) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2100) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (699), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2298) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2301) aNaturalNumber0(xm) = all_20_0_22
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5775) all_72_1_100 = all_20_0_22
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1244,5775) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1828) all_20_0_22 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1828,5775) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1244) all_72_1_100 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2301) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (780), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1787) and (2366) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5783) all_37_3_64 = all_20_2_24
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1233,5783) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1787) all_20_2_24 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1787,5783) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1233) all_37_3_64 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1787) and (2369) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (556), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2105) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2108) aNaturalNumber0(xp) = all_22_2_27
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5791) all_72_3_102 = all_22_2_27
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1243,5791) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1788) all_22_2_27 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2108) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (603), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2105) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2108) aNaturalNumber0(xp) = all_22_2_27
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5798) all_52_1_86 = all_22_2_27
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1238,5798) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2108) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1010), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2446) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2449) aNaturalNumber0(xn) = all_20_0_22
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5805) all_39_8_74 = all_20_0_22
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1179,5805) yields a new equation:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2449) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (878), into two cases.
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (2366) follows:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.08/171.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5812) all_20_2_24 = all_14_1_14
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1787,5812) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1218) all_14_1_14 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1218,5812) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1787) all_20_2_24 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (2369) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (797), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1828) and (2298) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2301) aNaturalNumber0(xm) = all_20_0_22
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5820) all_22_1_26 = all_20_0_22
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1229,5820) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1828) all_20_0_22 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1828,5820) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1229) all_22_1_26 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1828) and (2301) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (365), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (5464) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1775) and (1780) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5828) all_82_2_109 = all_22_2_27
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1830,5828) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1788) all_22_2_27 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1788,5828) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (5467) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (896), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (1939) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1942) aNaturalNumber0(xm) = all_62_2_94
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5836) all_62_2_94 = all_12_1_11
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (1942) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (768), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1281) and (1969) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1972) aNaturalNumber0(xm) = all_12_0_10
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5842) all_39_7_73 = all_12_0_10
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1236,5842) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1281) and (1972) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (750), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1674) and (3035) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5849) all_52_2_87 = all_47_1_82
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1674) and (3038) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (475), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2218)  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2218) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1284) and (2090) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2221) aNaturalNumber0(all_0_9_9) = all_20_2_24
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5855) all_24_2_30 = all_20_2_24
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1282,5855) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2221) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (668), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1789) and (2186) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2189) aNaturalNumber0(xp) = all_57_2_90
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5862) all_57_2_90 = all_26_1_32
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1789,5862) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1202) all_26_1_32 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1202,5862) yields a new equation:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1789) all_57_2_90 = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1789) and (2189) follows:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1079), into two cases.
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5866)  ~ (aNaturalNumber0(sz10) = all_16_2_18)
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1225) and (5866) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (61) and (1994) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5869) aNaturalNumber0(sz10) = all_16_2_18
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1225) all_16_2_18 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1225) and (5869) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (61) aNaturalNumber0(sz10) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (740), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1790) and (1939) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1942) aNaturalNumber0(xm) = all_62_2_94
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5876) all_62_2_94 = all_47_1_82
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1790) and (1942) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (598), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (2665) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2668) aNaturalNumber0(xp) = all_67_2_97
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5882) all_67_2_97 = all_52_1_86
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1829,5882) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1238) all_52_1_86 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1238,5882) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (2668) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (681), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2171) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5890) all_24_1_29 = all_20_0_22
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1207,5890) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1828) all_20_0_22 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2174) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (721), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1945) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5897) all_67_1_96 = all_57_2_90
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1242,5897) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1789) all_57_2_90 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1789,5897) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1242) all_67_1_96 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1948) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (819), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1945) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5905) all_57_2_90 = all_20_1_23
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1789,5905) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1228) all_20_1_23 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1228,5905) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1789) all_57_2_90 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1948) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (821), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2366) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5913) all_20_1_23 = all_20_2_24
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1228,5913) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1787) all_20_2_24 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2369) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (894), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2298) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2301) aNaturalNumber0(xm) = all_20_0_22
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5920) all_20_0_22 = all_12_1_11
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1828,5920) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1221) all_12_1_11 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1221,5920) yields a new equation:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2301) follows:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (467), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1284) and (2090) yields:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (872), into two cases.
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (4124) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5932) all_67_2_97 = all_14_1_14
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1829,5932) yields a new equation:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1218) all_14_1_14 = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1218,5932) yields a new equation:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1829) all_67_2_97 = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (4127) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (863), into two cases.
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2136) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2139) aNaturalNumber0(xm) = all_24_0_28
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5940) all_24_0_28 = all_16_1_17
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1350,5940) yields a new equation:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (848) all_16_1_17 = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (848,5940) yields a new equation:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1350) all_24_0_28 = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2139) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1018), into two cases.
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (2552) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2555) aNaturalNumber0(xn) = all_52_2_87
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5948) all_52_2_87 = all_39_8_74
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (5948,1674) yields a new equation:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5949) all_39_8_74 = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 5949 yields:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1179) all_39_8_74 = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (2555) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (769), into two cases.
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1674) and (3035) follows:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.08/171.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5956) all_52_2_87 = all_39_7_73
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1674) and (3038) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (895), into two cases.
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1791) and (1977) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1980) aNaturalNumber0(xm) = all_72_2_101
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5962) all_72_2_101 = all_12_1_11
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1791,5962) yields a new equation:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1221) all_12_1_11 = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1221,5962) yields a new equation:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1791) all_72_2_101 = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1791) and (1980) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (591), into two cases.
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2159) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5970) all_57_3_91 = all_47_2_83
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (2199,5970) yields a new equation:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1293,5970) yields a new equation:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2199) all_57_3_91 = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2162) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (816), into two cases.
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2298) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2301) aNaturalNumber0(xm) = all_20_0_22
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5978) all_20_0_22 = all_20_1_23
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1828,5978) yields a new equation:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1228) all_20_1_23 = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1228,5978) yields a new equation:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1828) all_20_0_22 = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2301) follows:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1058), into two cases.
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2120) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2123) aNaturalNumber0(xn) = all_67_2_97
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5986) all_67_2_97 = all_18_2_21
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,5986) yields a new equation:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1226) all_18_2_21 = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1226,5986) yields a new equation:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2123) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (975), into two cases.
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1228) and (2055) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2058) aNaturalNumber0(xn) = all_20_1_23
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5994) all_62_1_93 = all_20_1_23
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1240,5994) yields a new equation:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1228) all_20_1_23 = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1228,5994) yields a new equation:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1240) all_62_1_93 = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1228) and (2058) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (526), into two cases.
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1787) and (2031) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6002) all_82_3_110 = all_20_2_24
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1247,6002) yields a new equation:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1787) all_20_2_24 = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1787,6002) yields a new equation:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1247) all_82_3_110 = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1787) and (2034) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (621), into two cases.
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (3339) follows:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.08/171.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6010) all_77_2_105 = all_47_3_84
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1294,6010) yields a new equation:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2191) all_47_3_84 = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (2191,6010) yields a new equation:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1294) all_77_2_105 = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (3342) follows:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (712), into two cases.
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1674) and (3035) follows:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6018) all_72_1_100 = all_52_2_87
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1244,6018) yields a new equation:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1674) all_52_2_87 = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1674,6018) yields a new equation:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1244) all_72_1_100 = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1674) and (3038) follows:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (741), into two cases.
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1945) follows:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6026) all_57_2_90 = all_47_1_82
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1789,6026) yields a new equation:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1237) all_47_1_82 = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1237,6026) yields a new equation:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1789) all_57_2_90 = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1948) follows:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (434), into two cases.
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6030)  ~ (aNaturalNumber0(all_0_8_8) = all_20_0_22)
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (6030) follows:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1351) and (2575) yields:
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.08/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.43/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6033) aNaturalNumber0(all_0_8_8) = all_20_0_22
% 222.43/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6034) all_24_0_28 = all_20_0_22
% 222.43/171.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1350,6034) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1828) all_20_0_22 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1828,6034) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (6033) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1351) aNaturalNumber0(all_0_8_8) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (541), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2031) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6042) all_77_3_106 = all_20_2_24
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1245,6042) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1787) all_20_2_24 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1787,6042) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1245) all_77_3_106 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2034) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (962), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1293) and (2061) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2064) aNaturalNumber0(xn) = all_47_2_83
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6050) all_62_1_93 = all_47_2_83
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1240,6050) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1293) all_47_2_83 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1293) and (2064) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (739), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (1977) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1980) aNaturalNumber0(xm) = all_72_2_101
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6057) all_72_2_101 = all_47_1_82
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1791,6057) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1237) all_47_1_82 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1237,6057) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1791) all_72_2_101 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (1980) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (846), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (3035) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6065) all_52_2_87 = all_18_1_20
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (3038) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (783), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1292) and (3485) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6071) all_37_3_64 = all_16_0_16
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1233,6071) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1292) all_16_0_16 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1292,6071) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1233) all_37_3_64 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1292) and (3488) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (904), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1283) and (3028) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3031) aNaturalNumber0(xm) = all_26_2_33
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6079) all_26_2_33 = all_12_1_11
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1283,6079) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1221) all_12_1_11 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1221,6079) yields a new equation:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1283) all_26_2_33 = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1283) and (3031) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1072), into two cases.
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1229) and (2891) follows:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2894) aNaturalNumber0(xn) = all_22_1_26
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6087) all_22_1_26 = all_18_2_21
% 222.43/171.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1229,6087) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1226) all_18_2_21 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1226,6087) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1229) all_22_1_26 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1229) and (2894) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (736), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (2097) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6095) all_82_2_109 = all_47_1_82
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1830,6095) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1237) all_47_1_82 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1237,6095) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1830) all_82_2_109 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (2100) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (993), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (2552) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2555) aNaturalNumber0(xn) = all_52_2_87
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6103) all_57_1_89 = all_52_2_87
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (980,6103) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1674) all_52_2_87 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1674,6103) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (980) all_57_1_89 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (2555) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (859), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1787) and (2366) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6111) all_20_2_24 = all_16_1_17
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1787,6111) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (848) all_16_1_17 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (848,6111) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1787) all_20_2_24 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1787) and (2369) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (900), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (2275) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2278) aNaturalNumber0(xm) = all_77_2_105
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6119) all_77_2_105 = all_12_1_11
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1294,6119) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1221) all_12_1_11 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1221,6119) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (2278) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (361), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1788) and (2144) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1788) all_22_2_27 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1788) and (2147) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1015), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1283) and (2252) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2255) aNaturalNumber0(xn) = all_26_2_33
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6133) all_39_8_74 = all_26_2_33
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1179,6133) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1283) all_26_2_33 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1283,6133) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1179) all_39_8_74 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1283) and (2255) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (757), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (1977) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1980) aNaturalNumber0(xm) = all_72_2_101
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6141) all_72_2_101 = all_39_7_73
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1791,6141) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1236) all_39_7_73 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1236,6141) yields a new equation:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (1980) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (316), into two cases.
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1829) and (2665) follows:
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2668) aNaturalNumber0(xp) = all_67_2_97
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1829) all_67_2_97 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1829) and (2668) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1046), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1236) and (2522) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2525) aNaturalNumber0(xn) = all_39_7_73
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6155) all_39_7_73 = all_37_4_65
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1236,6155) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1232) all_37_4_65 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1232,6155) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1236) all_39_7_73 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1236) and (2525) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (969), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1244) and (2604) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2607) aNaturalNumber0(xn) = all_72_1_100
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6163) all_72_1_100 = all_62_1_93
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1244,6163) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1240) all_62_1_93 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1240,6163) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1244) all_72_1_100 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1244) and (2607) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (442), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6167)  ~ (aNaturalNumber0(all_0_8_8) = all_16_0_16)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1292) and (6167) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1351) and (2575) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6170) aNaturalNumber0(all_0_8_8) = all_16_0_16
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6171) all_24_0_28 = all_16_0_16
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1350,6171) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1292) and (6170) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1351) aNaturalNumber0(all_0_8_8) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1133), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1828) and (2446) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2449) aNaturalNumber0(xn) = all_20_0_22
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6178) all_20_0_22 = all_12_2_12
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1828,6178) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1223) all_12_2_12 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1223,6178) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1828) all_20_0_22 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1828) and (2449) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (890), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6182)  ~ (aNaturalNumber0(sz10) = all_12_1_11)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1221) and (6182) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6185) aNaturalNumber0(sz10) = all_12_1_11
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1221) all_12_1_11 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1221) and (6185) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (539), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1789) and (2186) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2189) aNaturalNumber0(xp) = all_57_2_90
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6192) all_77_3_106 = all_57_2_90
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1245,6192) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1789) all_57_2_90 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1789,6192) yields a new equation:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1245) all_77_3_106 = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1789) and (2189) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (838), into two cases.
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1787) and (2366) follows:
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6200) all_20_2_24 = all_18_1_20
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1787,6200) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1227) all_18_1_20 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1227,6200) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1787) all_20_2_24 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1787) and (2369) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (457), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2326)  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (2326) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1284) and (2090) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2329) aNaturalNumber0(all_0_9_9) = all_77_2_105
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6208) all_77_2_105 = all_26_2_33
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1294,6208) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1283) all_26_2_33 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1283,6208) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1294) all_77_2_105 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (2329) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (320), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6212)  ~ (aNaturalNumber0(sz00) = all_67_2_97)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (6212) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (26) and (2070) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6215) aNaturalNumber0(sz00) = all_67_2_97
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (6215) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (26) aNaturalNumber0(sz00) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1117), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1244) and (2604) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2607) aNaturalNumber0(xn) = all_72_1_100
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6222) all_72_1_100 = all_14_2_15
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1244,6222) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1200) all_14_2_15 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1200,6222) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1244) all_72_1_100 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1244) and (2607) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1125), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (848) and (2268) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2271) aNaturalNumber0(xn) = all_16_1_17
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6230) all_16_1_17 = all_14_2_15
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (848) and (2271) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (451), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2178)  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2178) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1284) and (2090) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2181) aNaturalNumber0(all_0_9_9) = all_20_0_22
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6236) all_26_2_33 = all_20_0_22
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1283,6236) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1828) all_20_0_22 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1828,6236) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1283) all_26_2_33 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2181) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (794), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6240)  ~ (aNaturalNumber0(sz00) = all_22_1_26)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1229) and (6240) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (26) and (2070) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6243) aNaturalNumber0(sz00) = all_22_1_26
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1229) all_22_1_26 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1229) and (6243) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1033), into two cases.
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (2120) follows:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2123) aNaturalNumber0(xn) = all_67_2_97
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6250) all_67_2_97 = all_37_4_65
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1829,6250) yields a new equation:
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1232) all_37_4_65 = 0
% 222.43/171.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1232,6250) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (2123) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (857), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1945) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6258) all_57_2_90 = all_16_1_17
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1789,6258) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (848) all_16_1_17 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (848,6258) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1789) all_57_2_90 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1948) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (311), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2151) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2154) aNaturalNumber0(xn) = all_82_2_109
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2154) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (949), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1229) and (2891) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2894) aNaturalNumber0(xn) = all_22_1_26
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6272) all_77_1_104 = all_22_1_26
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1246,6272) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1229) all_22_1_26 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1229,6272) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1246) all_77_1_104 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1229) and (2894) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (832), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (4124) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6280) all_67_2_97 = all_18_1_20
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,6280) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1227) all_18_1_20 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1227,6280) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (4127) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (860), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1294) and (2275) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2278) aNaturalNumber0(xm) = all_77_2_105
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6288) all_77_2_105 = all_16_1_17
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1294,6288) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (848) all_16_1_17 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (848,6288) yields a new equation:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1294) and (2278) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (369), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6292)  ~ (aNaturalNumber0(xr) = all_20_2_24)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1931)(1787) and (6292) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1665) and (1670) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6295) aNaturalNumber0(xr) = all_20_2_24
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1787) all_20_2_24 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1931)(1787) and (6295) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1665) aNaturalNumber0(xk) = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (446), into two cases.
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6298)  ~ (aNaturalNumber0(sz10) = all_26_2_33)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1283) and (6298) follows:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6301) aNaturalNumber0(sz10) = all_26_2_33
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1283) all_26_2_33 = 0
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1283) and (6301) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1066), into two cases.
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (2552) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2555) aNaturalNumber0(xn) = all_52_2_87
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6308) all_52_2_87 = all_18_2_21
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (6308,1674) yields a new equation:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6309) all_18_2_21 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 6309 yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1226) all_18_2_21 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (2555) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (489), into two cases.
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6312)  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (6312) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1284) and (2090) yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6315) aNaturalNumber0(all_0_9_9) = all_67_2_97
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6316) all_67_2_97 = all_12_0_10
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,6316) yields a new equation:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1281,6316) yields a new equation:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (6315) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (948), into two cases.
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1233) and (3295) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3298) aNaturalNumber0(xn) = all_37_3_64
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6324) all_77_1_104 = all_37_3_64
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1246,6324) yields a new equation:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1233) all_37_3_64 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1233,6324) yields a new equation:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1246) all_77_1_104 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1233) and (3298) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (331), into two cases.
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6328)  ~ (aNaturalNumber0(xr) = all_72_2_101)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1931)(1791) and (6328) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1665) and (1670) yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6331) aNaturalNumber0(xr) = all_72_2_101
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1791) all_72_2_101 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1931)(1791) and (6331) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1665) aNaturalNumber0(xk) = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (502), into two cases.
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (3035) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1674) all_52_2_87 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (3038) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (447), into two cases.
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6340)  ~ (aNaturalNumber0(sz00) = all_26_2_33)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1283) and (6340) follows:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (26) and (2070) yields:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6343) aNaturalNumber0(sz00) = all_26_2_33
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.43/171.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1283) and (6343) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (26) aNaturalNumber0(sz00) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (922), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1242) and (2334) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2337) aNaturalNumber0(xn) = all_67_1_96
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6350) all_82_1_108 = all_67_1_96
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1249,6350) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1242) all_67_1_96 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1242,6350) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1249) all_82_1_108 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1242) and (2337) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (707), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1292) and (3485) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6358) all_72_1_100 = all_16_0_16
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1244,6358) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1292) all_16_0_16 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1292,6358) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1244) all_72_1_100 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1292) and (3488) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1099), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1227) and (1933) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1936) aNaturalNumber0(xn) = all_18_1_20
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6366) all_18_1_20 = all_16_2_18
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1227,6366) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1225) all_16_2_18 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1225,6366) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1227) all_18_1_20 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1227) and (1936) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1091), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1674) and (2552) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2555) aNaturalNumber0(xn) = all_52_2_87
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6374) all_52_2_87 = all_16_2_18
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1674) and (2555) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1007), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6376)  ~ (aNaturalNumber0(sz00) = all_39_8_74)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1179) and (6376) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (26) and (2070) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6379) aNaturalNumber0(sz00) = all_39_8_74
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1179) all_39_8_74 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1179) and (6379) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (26) aNaturalNumber0(sz00) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1039), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1283) and (2252) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2255) aNaturalNumber0(xn) = all_26_2_33
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6386) all_37_4_65 = all_26_2_33
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1232,6386) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1283) all_26_2_33 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1283,6386) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1232) all_37_4_65 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1283) and (2255) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (432), into two cases.
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6390)  ~ (aNaturalNumber0(all_0_8_8) = all_82_2_109)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1830) and (6390) follows:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1351) and (2575) yields:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6393) aNaturalNumber0(all_0_8_8) = all_82_2_109
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6394) all_82_2_109 = all_24_0_28
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1830,6394) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1350,6394) yields a new equation:
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1830) all_82_2_109 = 0
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1830) and (6393) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1351) aNaturalNumber0(all_0_8_8) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1053), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1221) and (2081) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2084) aNaturalNumber0(xn) = all_12_1_11
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6402) all_37_4_65 = all_12_1_11
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1232,6402) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1221) all_12_1_11 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1221,6402) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1232) all_37_4_65 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1221) and (2084) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (569), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (2642) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2645) aNaturalNumber0(xp) = all_72_2_101
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6410) all_72_2_101 = all_67_3_98
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1791,6410) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1241) all_67_3_98 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1241,6410) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1791) all_72_2_101 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (2645) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (944), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (2552) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2555) aNaturalNumber0(xn) = all_52_2_87
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6418) all_77_1_104 = all_52_2_87
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1246,6418) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1674) all_52_2_87 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1674,6418) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1246) all_77_1_104 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (2555) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (935), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1829) and (2120) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2123) aNaturalNumber0(xn) = all_67_2_97
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6426) all_77_1_104 = all_67_2_97
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1246,6426) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1829) all_67_2_97 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1829,6426) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1246) all_77_1_104 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1829) and (2123) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (491), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5216)  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1791) and (5216) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1284) and (2090) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5219) aNaturalNumber0(all_0_9_9) = all_72_2_101
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6434) all_72_2_101 = all_12_0_10
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1791,6434) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1281,6434) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1791) all_72_2_101 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1791) and (5219) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (550), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (2112) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6442) all_82_2_109 = all_72_3_102
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1830,6442) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1243) all_72_3_102 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1243,6442) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1830) all_82_2_109 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (2115) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (959), into two cases.
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (2120) follows:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2123) aNaturalNumber0(xn) = all_67_2_97
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6450) all_67_2_97 = all_62_1_93
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1829,6450) yields a new equation:
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1240) all_62_1_93 = 0
% 222.43/171.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1240,6450) yields a new equation:
% 222.43/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1829) all_67_2_97 = 0
% 222.43/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.43/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (2123) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (337), into two cases.
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (5464) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1775) and (1780) yields:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6458) all_82_2_109 = all_72_2_101
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1830,6458) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1791) all_72_2_101 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1791,6458) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1830) all_82_2_109 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (5467) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (759), into two cases.
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1789) and (1945) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6466) all_57_2_90 = all_39_7_73
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1789,6466) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1236) all_39_7_73 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1236,6466) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1789) all_57_2_90 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1789) and (1948) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (505), into two cases.
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6470)  ~ (aNaturalNumber0(xk) = all_67_2_97)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (6470) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1665) and (1670) yields:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6473) aNaturalNumber0(xk) = all_67_2_97
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6474) all_67_2_97 = all_52_2_87
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,6474) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1674) all_52_2_87 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1674,6474) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (6473) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (630), into two cases.
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2112) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6482) all_82_2_109 = all_39_6_72
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1830,6482) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (629) all_39_6_72 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (629,6482) yields a new equation:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2115) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (908), into two cases.
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6486)  ~ (aNaturalNumber0(sz10) = all_82_1_108)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1249) and (6486) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (61) and (1994) yields:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6489) aNaturalNumber0(sz10) = all_82_1_108
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1249) all_82_1_108 = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1249) and (6489) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (61) aNaturalNumber0(sz10) = 0
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (558), into two cases.
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1294) and (3339) follows:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.57/171.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6496) all_77_2_105 = all_72_3_102
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1294,6496) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1243) all_72_3_102 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1243,6496) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1294) all_77_2_105 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1294) and (3342) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (633), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (2642) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2645) aNaturalNumber0(xp) = all_72_2_101
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6504) all_72_2_101 = all_39_6_72
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1791,6504) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (629) all_39_6_72 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (629,6504) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (2645) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (523), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (2506) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2509) aNaturalNumber0(xp) = all_62_2_94
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6512) all_82_3_110 = all_62_2_94
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1247,6512) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1790) all_62_2_94 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1790,6512) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1247) all_82_3_110 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (2509) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1149), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1227) and (1933) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1936) aNaturalNumber0(xn) = all_18_1_20
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6520) all_18_1_20 = all_12_2_12
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1227,6520) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1223) all_12_2_12 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1223,6520) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1227) all_18_1_20 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1227) and (1936) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1145), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1236) and (2522) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2525) aNaturalNumber0(xn) = all_39_7_73
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6528) all_39_7_73 = all_12_2_12
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1236,6528) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1223) all_12_2_12 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1223,6528) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1236) all_39_7_73 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1236) and (2525) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (893), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (4124) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6536) all_67_2_97 = all_12_1_11
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1829,6536) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1221) all_12_1_11 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1221,6536) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1829) all_67_2_97 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (4127) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (493), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2558)  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1789) and (2558) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1284) and (2090) yields:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2561) aNaturalNumber0(all_0_9_9) = all_57_2_90
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6544) all_57_2_90 = all_12_0_10
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1789,6544) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1281,6544) yields a new equation:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1789) all_57_2_90 = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1789) and (2561) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (906), into two cases.
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (1969) follows:
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1972) aNaturalNumber0(xm) = all_12_0_10
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6552) all_12_0_10 = all_12_1_11
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1281,6552) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1221) all_12_1_11 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1221,6552) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1281) all_12_0_10 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1281) and (1972) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (814), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2097) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6560) all_82_2_109 = all_20_1_23
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1830,6560) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1228) all_20_1_23 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1228,6560) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1830) all_82_2_109 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2100) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (593), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1350) and (2899) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2902) aNaturalNumber0(xp) = all_24_0_28
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6568) all_57_3_91 = all_24_0_28
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (2199,6568) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1350,6568) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2199) all_57_3_91 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1350) and (2902) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (826), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (3035) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6576) all_52_2_87 = all_20_1_23
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (3038) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (537), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1791) and (2642) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2645) aNaturalNumber0(xp) = all_72_2_101
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6582) all_77_3_106 = all_72_2_101
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1245,6582) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1791) all_72_2_101 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1791,6582) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1245) all_77_3_106 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1791) and (2645) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (820), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1788) and (2144) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6590) all_22_2_27 = all_20_1_23
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1788) and (2147) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (566), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2112) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6596) all_82_2_109 = all_67_3_98
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1830,6596) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1241) all_67_3_98 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1241,6596) yields a new equation:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1830) all_82_2_109 = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2115) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (818), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1790) and (1939) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1942) aNaturalNumber0(xm) = all_62_2_94
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6604) all_62_2_94 = all_20_1_23
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1790) and (1942) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (700), into two cases.
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1791) and (1977) follows:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1980) aNaturalNumber0(xm) = all_72_2_101
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6610) all_72_1_100 = all_72_2_101
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1244,6610) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1791) all_72_2_101 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1791,6610) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1244) all_72_1_100 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1791) and (1980) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (852), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2097) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6618) all_82_2_109 = all_16_1_17
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1830,6618) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (848) all_16_1_17 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (848,6618) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2100) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (309), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2112) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2115) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (347), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (5480) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1775) and (1780) yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6632) all_67_2_97 = all_62_2_94
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,6632) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1790) all_62_2_94 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1790,6632) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (5483) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (508), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6636)  ~ (aNaturalNumber0(xk) = all_62_2_94)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (6636) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1665) and (1670) yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6639) aNaturalNumber0(xk) = all_62_2_94
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6640) all_62_2_94 = all_52_2_87
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (6640,1790) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6641) all_52_2_87 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Simplifying 6641 yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1674) all_52_2_87 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (6639) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (333), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (1977) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1980) aNaturalNumber0(xm) = all_72_2_101
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1791) all_72_2_101 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (1980) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (958), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (2151) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2154) aNaturalNumber0(xn) = all_82_2_109
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6654) all_82_2_109 = all_62_1_93
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1830,6654) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1240) all_62_1_93 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1240,6654) yields a new equation:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1830) all_82_2_109 = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (2154) follows:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (340), into two cases.
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6658)  ~ (aNaturalNumber0(xr) = all_62_2_94)
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1931)(1790) and (6658) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1665) and (1670) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6661) aNaturalNumber0(xr) = all_62_2_94
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1790) all_62_2_94 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1931)(1790) and (6661) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (552), into two cases.
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2171) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6668) all_72_3_102 = all_20_0_22
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1243,6668) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1828) all_20_0_22 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1828,6668) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1243) all_72_3_102 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2174) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (646), into two cases.
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2665) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2668) aNaturalNumber0(xp) = all_67_2_97
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6676) all_67_2_97 = all_37_2_63
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,6676) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1195) all_37_2_63 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1195,6676) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2668) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (308), into two cases.
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6680)  ~ (aNaturalNumber0(xr) = all_82_2_109)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1931)(1830) and (6680) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1665) and (1670) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6683) aNaturalNumber0(xr) = all_82_2_109
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1830) all_82_2_109 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1931)(1830) and (6683) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1081), into two cases.
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (2151) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2154) aNaturalNumber0(xn) = all_82_2_109
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6690) all_82_2_109 = all_16_2_18
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1830,6690) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1225) all_16_2_18 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1225,6690) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1830) all_82_2_109 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (2154) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (654), into two cases.
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2159) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6698) all_47_2_83 = all_37_2_63
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,6698) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1195) all_37_2_63 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1195,6698) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2162) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (638), into two cases.
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (3339) follows:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6706) all_77_2_105 = all_39_6_72
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1294,6706) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (629) all_39_6_72 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (629,6706) yields a new equation:
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (3342) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1034), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2446) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2449) aNaturalNumber0(xn) = all_20_0_22
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6714) all_37_4_65 = all_20_0_22
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1232,6714) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1828) all_20_0_22 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1828,6714) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1232) all_37_4_65 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2449) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1111), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1292) and (2984) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2987) aNaturalNumber0(xn) = all_16_0_16
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6722) all_16_0_16 = all_14_2_15
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1292,6722) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1200) all_14_2_15 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1200,6722) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1292) all_16_0_16 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1292) and (2987) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (538), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1790) and (2506) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2509) aNaturalNumber0(xp) = all_62_2_94
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6730) all_77_3_106 = all_62_2_94
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1245,6730) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1790) all_62_2_94 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1790) and (2509) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1017), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1281) and (2374) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2377) aNaturalNumber0(xn) = all_12_0_10
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6737) all_39_8_74 = all_12_0_10
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1179,6737) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1281) all_12_0_10 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1281,6737) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1179) all_39_8_74 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1281) and (2377) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (773), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2097) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6745) all_82_2_109 = all_37_3_64
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,6745) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1233) all_37_3_64 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1233,6745) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2100) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1126), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1218) and (3165) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3168) aNaturalNumber0(xn) = all_14_1_14
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6753) all_14_1_14 = all_14_2_15
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1218) and (3168) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (620), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2031) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6759) all_47_3_84 = all_20_2_24
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (2191,6759) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1787) all_20_2_24 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1787,6759) yields a new equation:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2191) all_47_3_84 = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2034) follows:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (932), into two cases.
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6763)  ~ (aNaturalNumber0(sz10) = all_77_1_104)
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1246) and (6763) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (61) and (1994) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6766) aNaturalNumber0(sz10) = all_77_1_104
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1246) all_77_1_104 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1246) and (6766) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (61) aNaturalNumber0(sz10) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (555), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1789) and (2186) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2189) aNaturalNumber0(xp) = all_57_2_90
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6773) all_72_3_102 = all_57_2_90
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1243,6773) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1789) all_57_2_90 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1789,6773) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1243) all_72_3_102 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1789) and (2189) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (676), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1282) and (2475) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2478) aNaturalNumber0(xp) = all_24_2_30
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6781) all_26_1_32 = all_24_2_30
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1202,6781) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1282) all_24_2_30 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1282,6781) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1202) all_26_1_32 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1282) and (2478) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (815), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1829) and (4124) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6789) all_67_2_97 = all_20_1_23
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1829,6789) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1228) all_20_1_23 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1228,6789) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1829) all_67_2_97 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1829) and (4127) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (840), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2962) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6797) all_47_2_83 = all_18_1_20
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1293,6797) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1227) all_18_1_20 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1227,6797) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2965) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (684), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (2186) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2189) aNaturalNumber0(xp) = all_57_2_90
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6805) all_57_2_90 = all_24_1_29
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1789,6805) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1207) all_24_1_29 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1207,6805) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1789) all_57_2_90 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (2189) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (766), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (3028) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3031) aNaturalNumber0(xm) = all_26_2_33
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6813) all_39_7_73 = all_26_2_33
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1236,6813) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,6813) yields a new equation:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1236) all_39_7_73 = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (3031) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (589), into two cases.
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2031) follows:
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6821) all_57_3_91 = all_20_2_24
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (2199,6821) yields a new equation:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1787) all_20_2_24 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2034) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (514), into two cases.
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6824)  ~ (aNaturalNumber0(xk) = all_16_0_16)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (6824) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1665) and (1670) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6827) aNaturalNumber0(xk) = all_16_0_16
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6828) all_52_2_87 = all_16_0_16
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1674,6828) yields a new equation:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1292) all_16_0_16 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (6827) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (632), into two cases.
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2171) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6835) all_39_6_72 = all_20_0_22
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (629,6835) yields a new equation:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1828) all_20_0_22 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2174) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (957), into two cases.
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6838)  ~ (aNaturalNumber0(sz00) = all_62_1_93)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1240) and (6838) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (26) and (2070) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6841) aNaturalNumber0(sz00) = all_62_1_93
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1240) all_62_1_93 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1240) and (6841) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (323), into two cases.
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6844)  ~ (aNaturalNumber0(xr) = all_20_0_22)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1931)(1828) and (6844) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1665) and (1670) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6847) aNaturalNumber0(xr) = all_20_0_22
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1828) all_20_0_22 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1931)(1828) and (6847) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (999), into two cases.
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1229) and (2891) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2894) aNaturalNumber0(xn) = all_22_1_26
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6854) all_57_1_89 = all_22_1_26
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (980,6854) yields a new equation:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1229) all_22_1_26 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1229,6854) yields a new equation:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (980) all_57_1_89 = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1229) and (2894) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (746), into two cases.
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (2136) follows:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2139) aNaturalNumber0(xm) = all_24_0_28
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6862) all_47_1_82 = all_24_0_28
% 222.57/171.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1237,6862) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1350) all_24_0_28 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1350,6862) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1237) all_47_1_82 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (2139) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (417), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4548)  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4548) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1295) and (2129) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4551) aNaturalNumber0(all_0_7_7) = all_67_2_97
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6870) all_67_2_97 = all_16_0_16
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,6870) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1292) all_16_0_16 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1292,6870) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4551) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1146), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1233) and (3295) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3298) aNaturalNumber0(xn) = all_37_3_64
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6878) all_37_3_64 = all_12_2_12
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1233,6878) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1223) all_12_2_12 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1223,6878) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1233) all_37_3_64 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1233) and (3298) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (501), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1665) and (1670) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1665) aNaturalNumber0(xk) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1674) all_52_2_87 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (355), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (5464) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1775) and (1780) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6890) all_82_2_109 = all_57_2_90
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1830,6890) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1789) all_57_2_90 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1789,6890) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1830) all_82_2_109 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (5467) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (623), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1292) and (2023) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2026) aNaturalNumber0(xp) = all_16_0_16
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6898) all_47_3_84 = all_16_0_16
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (2191,6898) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1292) all_16_0_16 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1292,6898) yields a new equation:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2191) all_47_3_84 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1292) and (2026) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1006), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6902)  ~ (aNaturalNumber0(sz10) = all_39_8_74)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1179) and (6902) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6905) aNaturalNumber0(sz10) = all_39_8_74
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1179) all_39_8_74 = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1179) and (6905) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (782), into two cases.
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2962) follows:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.57/171.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6912) all_47_2_83 = all_37_3_64
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1293,6912) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1233) all_37_3_64 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1233,6912) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2965) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (436), into two cases.
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6916)  ~ (aNaturalNumber0(all_0_8_8) = all_62_2_94)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1790) and (6916) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1351) and (2575) yields:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6919) aNaturalNumber0(all_0_8_8) = all_62_2_94
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6920) all_62_2_94 = all_24_0_28
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1790,6920) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1350,6920) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1790) all_62_2_94 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1790) and (6919) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1351) aNaturalNumber0(all_0_8_8) = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (710), into two cases.
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1282) and (2382) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2385) aNaturalNumber0(xm) = all_24_2_30
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6928) all_72_1_100 = all_24_2_30
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1244,6928) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1282) all_24_2_30 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1282,6928) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1244) all_72_1_100 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1282) and (2385) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1113), into two cases.
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (2252) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2255) aNaturalNumber0(xn) = all_26_2_33
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6936) all_26_2_33 = all_14_2_15
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (2255) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (727), into two cases.
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1350) and (2136) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2139) aNaturalNumber0(xm) = all_24_0_28
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6942) all_67_1_96 = all_24_0_28
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1242,6942) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1350) all_24_0_28 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1350,6942) yields a new equation:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1242) all_67_1_96 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1350) and (2139) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (869), into two cases.
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6946)  ~ (aNaturalNumber0(sz10) = all_14_1_14)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1218) and (6946) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (61) and (1994) yields:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6949) aNaturalNumber0(sz10) = all_14_1_14
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1218) all_14_1_14 = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1218) and (6949) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (61) aNaturalNumber0(sz10) = 0
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1031), into two cases.
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6952)  ~ (aNaturalNumber0(sz00) = all_37_4_65)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1232) and (6952) follows:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (26) and (2070) yields:
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.57/171.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6955) aNaturalNumber0(sz00) = all_37_4_65
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1232) all_37_4_65 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1232) and (6955) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (885), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1281) and (1969) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1972) aNaturalNumber0(xm) = all_12_0_10
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6962) all_14_1_14 = all_12_0_10
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (6962,1218) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2959) all_12_0_10 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Simplifying 2959 yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1281) all_12_0_10 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1281) and (1972) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (626), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2475) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2478) aNaturalNumber0(xp) = all_24_2_30
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6970) all_47_3_84 = all_24_2_30
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (2191,6970) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2478) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1074), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (848) and (2268) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2271) aNaturalNumber0(xn) = all_16_1_17
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6977) all_18_2_21 = all_16_1_17
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1226,6977) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (848) all_16_1_17 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (848) and (2271) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (658), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1282) and (2475) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2478) aNaturalNumber0(xp) = all_24_2_30
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6984) all_37_2_63 = all_24_2_30
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1195,6984) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1282) and (2478) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (366), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5480) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1775) and (1780) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6991) all_67_2_97 = all_22_2_27
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,6991) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1788,6991) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5483) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (990), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (2252) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2255) aNaturalNumber0(xn) = all_26_2_33
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6999) all_57_1_89 = all_26_2_33
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (980,6999) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1283) all_26_2_33 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1283,6999) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (980) all_57_1_89 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (2255) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (487), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1284) and (2090) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1098), into two cases.
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1228) and (2055) follows:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2058) aNaturalNumber0(xn) = all_20_1_23
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7011) all_20_1_23 = all_16_2_18
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1228,7011) yields a new equation:
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1225) all_16_2_18 = 0
% 222.57/171.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1225,7011) yields a new equation:
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1228) all_20_1_23 = 0
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1228) and (2058) follows:
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (488), into two cases.
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2290)  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2290) follows:
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1284) and (2090) yields:
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2293) aNaturalNumber0(all_0_9_9) = all_82_2_109
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7019) all_82_2_109 = all_12_0_10
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.57/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1830,7019) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1281) all_12_0_10 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1281,7019) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2293) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (702), into two cases.
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1789) and (1945) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7027) all_72_1_100 = all_57_2_90
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1244,7027) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1789) all_57_2_90 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1789,7027) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1244) all_72_1_100 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1789) and (1948) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (665), into two cases.
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2171) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7035) all_26_1_32 = all_20_0_22
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1202,7035) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2174) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (722), into two cases.
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1788) and (2144) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7042) all_67_1_96 = all_22_2_27
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1242,7042) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1788) all_22_2_27 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1788,7042) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1242) all_67_1_96 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1788) and (2147) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (516), into two cases.
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7046)  ~ (aNaturalNumber0(xk) = all_26_2_33)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (7046) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1665) and (1670) yields:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7049) aNaturalNumber0(xk) = all_26_2_33
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7050) all_52_2_87 = all_26_2_33
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1674,7050) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1283,7050) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1674) all_52_2_87 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1013), into two cases.
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2984) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2987) aNaturalNumber0(xn) = all_16_0_16
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7057) all_39_8_74 = all_16_0_16
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1179,7057) yields a new equation:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1292) all_16_0_16 = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2987) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (453), into two cases.
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4821)  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1790) and (4821) follows:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1284) and (2090) yields:
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.68/171.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4824) aNaturalNumber0(all_0_9_9) = all_62_2_94
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7064) all_62_2_94 = all_26_2_33
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1790,7064) yields a new equation:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1283) all_26_2_33 = 0
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1283,7064) yields a new equation:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1790) all_62_2_94 = 0
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1790) and (4824) follows:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (743), into two cases.
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1787) and (2366) follows:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7072) all_47_1_82 = all_20_2_24
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1237,7072) yields a new equation:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1787) all_20_2_24 = 0
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1787,7072) yields a new equation:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1237) all_47_1_82 = 0
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1787) and (2369) follows:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1011), into two cases.
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (1953) follows:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1956) aNaturalNumber0(xn) = all_77_2_105
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7080) all_77_2_105 = all_39_8_74
% 222.68/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1294,7080) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1179) all_39_8_74 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1179,7080) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1294) all_77_2_105 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (1956) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1112), into two cases.
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (1985) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1988) aNaturalNumber0(xn) = all_24_0_28
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7088) all_24_0_28 = all_14_2_15
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1350,7088) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1200) all_14_2_15 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1200,7088) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1350) all_24_0_28 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (1988) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (864), into two cases.
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1283) and (3028) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3031) aNaturalNumber0(xm) = all_26_2_33
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7096) all_26_2_33 = all_16_1_17
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1283,7096) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (848) all_16_1_17 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (848,7096) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1283) all_26_2_33 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1283) and (3031) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (334), into two cases.
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7100)  ~ (aNaturalNumber0(sz10) = all_72_2_101)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1791) and (7100) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (61) and (1994) yields:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7103) aNaturalNumber0(sz10) = all_72_2_101
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1791) and (7103) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (61) aNaturalNumber0(sz10) = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (920), into two cases.
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1674) and (2552) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2555) aNaturalNumber0(xn) = all_52_2_87
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7110) all_82_1_108 = all_52_2_87
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1249,7110) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1674) all_52_2_87 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1674,7110) yields a new equation:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1249) all_82_1_108 = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1674) and (2555) follows:
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (335), into two cases.
% 222.71/171.91  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7114)  ~ (aNaturalNumber0(sz00) = all_72_2_101)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (7114) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (26) and (2070) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7117) aNaturalNumber0(sz00) = all_72_2_101
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1791) all_72_2_101 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (7117) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (26) aNaturalNumber0(sz00) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (884), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1282) and (2382) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2385) aNaturalNumber0(xm) = all_24_2_30
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7124) all_24_2_30 = all_14_1_14
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1282,7124) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1218) all_14_1_14 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1218,7124) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1282) all_24_2_30 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1282) and (2385) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (336), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1775) and (1780) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1791) all_72_2_101 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (392), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2620)  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1788) and (2620) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1295) and (2129) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2623) aNaturalNumber0(all_0_7_7) = all_22_2_27
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7136) all_77_2_105 = all_22_2_27
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1294,7136) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1788) all_22_2_27 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1788,7136) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1294) all_77_2_105 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1788) and (2623) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (345), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1775) and (1780) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1790) all_62_2_94 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (380), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (3339) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1294) all_77_2_105 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (3342) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (575), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2159) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7154) all_67_3_98 = all_47_2_83
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1241,7154) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1293,7154) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1241) all_67_3_98 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2162) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (961), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1294) and (1953) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1956) aNaturalNumber0(xn) = all_77_2_105
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7162) all_77_2_105 = all_62_1_93
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1294,7162) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1240) all_62_1_93 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1240,7162) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1294) all_77_2_105 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1294) and (1956) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (576), into two cases.
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2023) follows:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2026) aNaturalNumber0(xp) = all_16_0_16
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7170) all_67_3_98 = all_16_0_16
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1241,7170) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1292) all_16_0_16 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1292,7170) yields a new equation:
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1241) all_67_3_98 = 0
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.92  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2026) follows:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (725), into two cases.
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1293) and (2962) follows:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7178) all_67_1_96 = all_47_2_83
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1242,7178) yields a new equation:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1293) all_47_2_83 = 0
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1293,7178) yields a new equation:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1242) all_67_1_96 = 0
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1293) and (2965) follows:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (579), into two cases.
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1282) and (2475) follows:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2478) aNaturalNumber0(xp) = all_24_2_30
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7186) all_67_3_98 = all_24_2_30
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1241,7186) yields a new equation:
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1282) all_24_2_30 = 0
% 222.71/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1282,7186) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1241) all_67_3_98 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1282) and (2478) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (450), into two cases.
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6312)  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (6312) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1284) and (2090) yields:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6315) aNaturalNumber0(all_0_9_9) = all_67_2_97
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7194) all_67_2_97 = all_26_2_33
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1829,7194) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1283) all_26_2_33 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1283,7194) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (6315) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (580), into two cases.
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1281) and (2039) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2042) aNaturalNumber0(xp) = all_12_0_10
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7202) all_67_3_98 = all_12_0_10
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1241,7202) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1281) all_12_0_10 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1281,7202) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1241) all_67_3_98 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1281) and (2042) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (462), into two cases.
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2475) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2478) aNaturalNumber0(xp) = all_24_2_30
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2478) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (875), into two cases.
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (1939) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1942) aNaturalNumber0(xm) = all_62_2_94
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7216) all_62_2_94 = all_14_1_14
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1790,7216) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1218) all_14_1_14 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1218,7216) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1790) all_62_2_94 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (1942) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (474), into two cases.
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2312)  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2312) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1284) and (2090) yields:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2315) aNaturalNumber0(all_0_9_9) = all_22_2_27
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7224) all_24_2_30 = all_22_2_27
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1282,7224) yields a new equation:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2315) follows:
% 222.72/171.93  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (825), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (1969) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1972) aNaturalNumber0(xm) = all_12_0_10
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7231) all_20_1_23 = all_12_0_10
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (7231,1228) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2959) all_12_0_10 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Simplifying 2959 yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (1972) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (444), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (3028) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3031) aNaturalNumber0(xm) = all_26_2_33
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1283) all_26_2_33 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (3031) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (779), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (2144) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7245) all_37_3_64 = all_22_2_27
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1233,7245) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1788) all_22_2_27 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (2147) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (439), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7248)  ~ (aNaturalNumber0(all_0_8_8) = all_20_2_24)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1787) and (7248) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1351) and (2575) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7251) aNaturalNumber0(all_0_8_8) = all_20_2_24
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7252) all_24_0_28 = all_20_2_24
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1350,7252) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1787) all_20_2_24 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1787) and (7251) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1351) aNaturalNumber0(all_0_8_8) = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (599), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2171) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7259) all_52_1_86 = all_20_0_22
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1238,7259) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1828) all_20_0_22 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1828,7259) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1238) all_52_1_86 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2174) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (435), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7263)  ~ (aNaturalNumber0(all_0_8_8) = all_72_2_101)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1791) and (7263) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1351) and (2575) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7266) aNaturalNumber0(all_0_8_8) = all_72_2_101
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7267) all_72_2_101 = all_24_0_28
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1791,7267) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1350,7267) yields a new equation:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1791) all_72_2_101 = 0
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (805), into two cases.
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1292) and (3485) follows:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.72/171.94  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7274) all_22_1_26 = all_16_0_16
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1229,7274) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1292) and (3488) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (404), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4226)  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1791) and (4226) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1295) and (2129) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4229) aNaturalNumber0(all_0_7_7) = all_72_2_101
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7281) all_72_2_101 = all_47_2_83
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1791,7281) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,7281) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1791) all_72_2_101 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1791) and (4229) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (426), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1350) and (2899) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2902) aNaturalNumber0(xp) = all_24_0_28
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1350) all_24_0_28 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1350) and (2902) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (858), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1788) and (2144) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7295) all_22_2_27 = all_16_1_17
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (7295,1788) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4239) all_16_1_17 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Simplifying 4239 yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (848) all_16_1_17 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1788) and (2147) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (429), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7299)  ~ (aNaturalNumber0(sz10) = all_24_0_28)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (7299) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (61) and (1994) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7302) aNaturalNumber0(sz10) = all_24_0_28
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1350) all_24_0_28 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (7302) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (61) aNaturalNumber0(sz10) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (469), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6312)  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (6312) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1284) and (2090) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6315) aNaturalNumber0(all_0_9_9) = all_67_2_97
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7309) all_67_2_97 = all_24_2_30
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1829,7309) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1282) all_24_2_30 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1282,7309) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (6315) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (385), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1295) and (2129) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1294) all_77_2_105 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1025), into two cases.
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1228) and (2055) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2058) aNaturalNumber0(xn) = all_20_1_23
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7321) all_39_8_74 = all_20_1_23
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1179,7321) yields a new equation:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1228) all_20_1_23 = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1228) and (2058) follows:
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.95  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (387), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4548)  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4548) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1295) and (2129) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4551) aNaturalNumber0(all_0_7_7) = all_67_2_97
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7328) all_77_2_105 = all_67_2_97
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,7328) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,7328) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4551) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (351), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1789) and (1945) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1789) all_57_2_90 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1789) and (1948) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (403), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2128)  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2128) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1295) and (2129) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2131) aNaturalNumber0(all_0_7_7) = all_20_0_22
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7342) all_47_2_83 = all_20_0_22
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1293,7342) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1828) all_20_0_22 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1828,7342) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1293) all_47_2_83 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2131) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (318), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (2120) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2123) aNaturalNumber0(xn) = all_67_2_97
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1829) all_67_2_97 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (2123) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (396), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1293) and (2962) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1293) all_47_2_83 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1293) and (2965) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (551), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1829) and (2665) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2668) aNaturalNumber0(xp) = all_67_2_97
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7362) all_72_3_102 = all_67_2_97
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1243,7362) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1829) all_67_2_97 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1829,7362) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1243) all_72_3_102 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1829) and (2668) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (390), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2755)  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (2755) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1295) and (2129) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2758) aNaturalNumber0(all_0_7_7) = all_62_2_94
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7370) all_77_2_105 = all_62_2_94
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1294,7370) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1790) all_62_2_94 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1790,7370) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1294) all_77_2_105 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (2758) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1108), into two cases.
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2446) follows:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2449) aNaturalNumber0(xn) = all_20_0_22
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7378) all_20_0_22 = all_14_2_15
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1828,7378) yields a new equation:
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1200) all_14_2_15 = 0
% 222.72/171.96  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1200,7378) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2449) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (421), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5022)  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (5022) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1295) and (2129) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5025) aNaturalNumber0(all_0_7_7) = all_57_2_90
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7386) all_57_2_90 = all_16_0_16
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1789,7386) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1292,7386) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1789) all_57_2_90 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (5025) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (703), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2144) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7394) all_72_1_100 = all_22_2_27
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1244,7394) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1788) all_22_2_27 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2147) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (411), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (3485) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (3488) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (582), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2112) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7407) all_82_2_109 = all_57_3_91
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1830,7407) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2199) all_57_3_91 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (2199,7407) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1830) all_82_2_109 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1830) and (2115) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (564), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (2039) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2042) aNaturalNumber0(xp) = all_12_0_10
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7415) all_72_3_102 = all_12_0_10
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1243,7415) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1281) all_12_0_10 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1281,7415) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1243) all_72_3_102 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (2042) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (314), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2426)  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1831) and (2426) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1831) aNaturalNumber0(all_0_2_2) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1002), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (848) and (2268) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2271) aNaturalNumber0(xn) = all_16_1_17
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7427) all_57_1_89 = all_16_1_17
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (980,7427) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (848) all_16_1_17 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (848) and (2271) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (521), into two cases.
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1828) and (2171) follows:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7434) all_82_3_110 = all_20_0_22
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1247,7434) yields a new equation:
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1828) all_20_0_22 = 0
% 222.72/171.97  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1828,7434) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1247) all_82_3_110 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1828) and (2174) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (418), into two cases.
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2128)  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2128) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1295) and (2129) yields:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2131) aNaturalNumber0(all_0_7_7) = all_20_0_22
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7442) all_20_0_22 = all_16_0_16
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1828,7442) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1292) all_16_0_16 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1292,7442) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1828) all_20_0_22 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2131) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1140), into two cases.
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1281) and (2374) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2377) aNaturalNumber0(xn) = all_12_0_10
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7450) all_12_0_10 = all_12_2_12
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1281,7450) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1223) all_12_2_12 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1223,7450) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1281) all_12_0_10 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1281) and (2377) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (419), into two cases.
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4226)  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (4226) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1295) and (2129) yields:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4229) aNaturalNumber0(all_0_7_7) = all_72_2_101
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7458) all_72_2_101 = all_16_0_16
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1791,7458) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1292,7458) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (4229) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (853), into two cases.
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (4124) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7466) all_67_2_97 = all_16_1_17
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1829,7466) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (848) all_16_1_17 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (848,7466) yields a new equation:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1829) all_67_2_97 = 0
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1829) and (4127) follows:
% 222.72/171.98  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (413), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7470)  ~ (aNaturalNumber0(sz10) = all_16_0_16)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1292) and (7470) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7473) aNaturalNumber0(sz10) = all_16_0_16
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1292) all_16_0_16 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (910), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2151) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2154) aNaturalNumber0(xn) = all_82_2_109
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7479) all_82_1_108 = all_82_2_109
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1249,7479) yields a new equation:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2154) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (972), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1236) and (2522) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2525) aNaturalNumber0(xn) = all_39_7_73
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7486) all_62_1_93 = all_39_7_73
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1240,7486) yields a new equation:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1236) all_39_7_73 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1236,7486) yields a new equation:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1240) all_62_1_93 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1236) and (2525) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (454), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2558)  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (2558) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1284) and (2090) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2561) aNaturalNumber0(all_0_9_9) = all_57_2_90
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7494) all_57_2_90 = all_26_2_33
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1789,7494) yields a new equation:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1283) all_26_2_33 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (412), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1292) and (2984) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2987) aNaturalNumber0(xn) = all_16_0_16
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1292) and (2987) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (718), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2298) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2301) aNaturalNumber0(xm) = all_20_0_22
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7506) all_67_1_96 = all_20_0_22
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1242,7506) yields a new equation:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1828) all_20_0_22 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1828,7506) yields a new equation:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1242) all_67_1_96 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2301) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (830), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7510)  ~ (aNaturalNumber0(sz00) = all_18_1_20)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1227) and (7510) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (26) and (2070) yields:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7513) aNaturalNumber0(sz00) = all_18_1_20
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1227) all_18_1_20 = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1227) and (7513) follows:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (26) aNaturalNumber0(sz00) = 0
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (774), into two cases.
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/171.99  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (4124) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7520) all_67_2_97 = all_37_3_64
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,7520) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1233) all_37_3_64 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1233,7520) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (4127) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (464), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1282) and (2210) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2213) aNaturalNumber0(xn) = all_24_2_30
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1282) all_24_2_30 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1282) and (2213) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (604), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1787) and (2031) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7534) all_52_1_86 = all_20_2_24
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1238,7534) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1787) all_20_2_24 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1787) and (2034) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (428), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (1985) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1988) aNaturalNumber0(xn) = all_24_0_28
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1350) all_24_0_28 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (1988) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (597), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2112) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7547) all_82_2_109 = all_52_1_86
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,7547) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1238) all_52_1_86 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1238,7547) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2115) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (393), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2883)  ~ (aNaturalNumber0(all_0_7_7) = all_20_2_24)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2883) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1295) and (2129) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2886) aNaturalNumber0(all_0_7_7) = all_20_2_24
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7555) all_77_2_105 = all_20_2_24
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,7555) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1787) all_20_2_24 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1787,7555) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2886) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (324), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2171) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1828) all_20_0_22 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2174) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (563), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (2475) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2478) aNaturalNumber0(xp) = all_24_2_30
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7569) all_72_3_102 = all_24_2_30
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1243,7569) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1282,7569) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1243) all_72_3_102 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (2478) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (983), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (2151) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2154) aNaturalNumber0(xn) = all_82_2_109
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7577) all_82_2_109 = all_57_1_89
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1830,7577) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (980) all_57_1_89 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (980,7577) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1830) all_82_2_109 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (2154) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (845), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (1969) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1972) aNaturalNumber0(xm) = all_12_0_10
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7585) all_18_1_20 = all_12_0_10
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1227,7585) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1281,7585) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1227) all_18_1_20 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (1972) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (886), into two cases.
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (3035) follows:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3038) aNaturalNumber0(xm) = all_52_2_87
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7593) all_52_2_87 = all_14_1_14
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1674,7593) yields a new equation:
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1218) all_14_1_14 = 0
% 222.72/172.00  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1218,7593) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1674) all_52_2_87 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (3038) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (329), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2426)  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1831) and (2426) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1831) aNaturalNumber0(all_0_2_2) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1828) all_20_0_22 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (796), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (4124) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4127) aNaturalNumber0(xm) = all_67_2_97
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7605) all_67_2_97 = all_22_1_26
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,7605) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1229) all_22_1_26 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1229,7605) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (4127) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (328), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7609)  ~ (aNaturalNumber0(sz00) = all_20_0_22)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (7609) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (26) and (2070) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7612) aNaturalNumber0(sz00) = all_20_0_22
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (572), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2105) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2108) aNaturalNumber0(xp) = all_22_2_27
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7618) all_67_3_98 = all_22_2_27
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1241,7618) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1788) all_22_2_27 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2108) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (611), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1281) and (2039) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2042) aNaturalNumber0(xp) = all_12_0_10
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7625) all_52_1_86 = all_12_0_10
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1238,7625) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1281) all_12_0_10 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1281,7625) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1238) all_52_1_86 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1281) and (2042) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (823), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (2136) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2139) aNaturalNumber0(xm) = all_24_0_28
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7633) all_24_0_28 = all_20_1_23
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1350,7633) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1228) all_20_1_23 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1228,7633) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1350) all_24_0_28 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (2139) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (608), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2899) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2902) aNaturalNumber0(xp) = all_24_0_28
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7641) all_52_1_86 = all_24_0_28
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1238,7641) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1350,7641) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1238) all_52_1_86 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2902) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (622), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1293) and (2159) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7649) all_47_2_83 = all_47_3_84
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1293,7649) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2191) all_47_3_84 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (2191,7649) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1293) all_47_2_83 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1293) and (2162) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (607), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1292) and (2023) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2026) aNaturalNumber0(xp) = all_16_0_16
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7657) all_52_1_86 = all_16_0_16
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1238,7657) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1292) all_16_0_16 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1292,7657) yields a new equation:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1238) all_52_1_86 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1292) and (2026) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (332), into two cases.
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (2642) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2645) aNaturalNumber0(xp) = all_72_2_101
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (2645) follows:
% 222.72/172.01  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (606), into two cases.
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1293) and (2159) follows:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7671) all_52_1_86 = all_47_2_83
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1238,7671) yields a new equation:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1293) all_47_2_83 = 0
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1293) and (2162) follows:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (905), into two cases.
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2382) follows:
% 222.72/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2385) aNaturalNumber0(xm) = all_24_2_30
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7678) all_24_2_30 = all_12_1_11
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1282,7678) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1221) all_12_1_11 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1221,7678) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2385) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (605), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1294) and (3339) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7686) all_77_2_105 = all_52_1_86
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1294,7686) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1238) all_52_1_86 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1238,7686) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1294) and (3342) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (360), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1788) and (2105) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2108) aNaturalNumber0(xp) = all_22_2_27
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1788) all_22_2_27 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1788) and (2108) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1093), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1242) and (2334) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2337) aNaturalNumber0(xn) = all_67_1_96
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7700) all_67_1_96 = all_16_2_18
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1242,7700) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1225) all_16_2_18 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1225,7700) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1242) all_67_1_96 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1242) and (2337) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (899), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1787) and (2366) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2369) aNaturalNumber0(xm) = all_20_2_24
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7708) all_20_2_24 = all_12_1_11
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1787,7708) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1221) all_12_1_11 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1221,7708) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1787) all_20_2_24 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1787) and (2369) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (841), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3485) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7716) all_18_1_20 = all_16_0_16
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (7716,1227) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2760) all_16_0_16 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Simplifying 2760 yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3488) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (527), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (3339) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7724) all_82_3_110 = all_77_2_105
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1247,7724) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1294) all_77_2_105 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (3342) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (416), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3255)  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (3255) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1295) and (2129) yields:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3258) aNaturalNumber0(all_0_7_7) = all_82_2_109
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7731) all_82_2_109 = all_16_0_16
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1830,7731) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1292,7731) yields a new equation:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1830) all_82_2_109 = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (3258) follows:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (559), into two cases.
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.02  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2159) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7739) all_72_3_102 = all_47_2_83
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1243,7739) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2162) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (861), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2962) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7746) all_47_2_83 = all_16_1_17
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1293,7746) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (848) all_16_1_17 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (848,7746) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2965) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1021), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1237) and (2490) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2493) aNaturalNumber0(xn) = all_47_1_82
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7754) all_47_1_82 = all_39_8_74
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1237,7754) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1179) all_39_8_74 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1179,7754) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1237) all_47_1_82 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1237) and (2493) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (954), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1221) and (2081) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2084) aNaturalNumber0(xn) = all_12_1_11
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7762) all_77_1_104 = all_12_1_11
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1246,7762) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1221) all_12_1_11 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1221) and (2084) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (960), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2446) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2449) aNaturalNumber0(xn) = all_20_0_22
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7769) all_62_1_93 = all_20_0_22
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (7769,1240) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2724) all_20_0_22 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Simplifying 2724 yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1828) all_20_0_22 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2449) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (400), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1295) and (2129) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1293) all_47_2_83 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (619), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2105) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2108) aNaturalNumber0(xp) = all_22_2_27
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7781) all_47_3_84 = all_22_2_27
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (7781,2191) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5091) all_22_2_27 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Simplifying 5091 yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1788) all_22_2_27 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2108) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (902), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1292) and (3485) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7789) all_16_0_16 = all_12_1_11
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1292) and (3488) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (356), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5480) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1775) and (1780) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7795) all_67_2_97 = all_57_2_90
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,7795) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1789,7795) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5483) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (871), into two cases.
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (2097) follows:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7803) all_82_2_109 = all_14_1_14
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1830,7803) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1218) all_14_1_14 = 0
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1218,7803) yields a new equation:
% 222.83/172.03  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1830) all_82_2_109 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (2100) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (883), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (3028) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3031) aNaturalNumber0(xm) = all_26_2_33
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7811) all_26_2_33 = all_14_1_14
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (3031) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1150), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (848) and (2268) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2271) aNaturalNumber0(xn) = all_16_1_17
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7817) all_16_1_17 = all_12_2_12
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (848) and (2271) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (882), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2136) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2139) aNaturalNumber0(xm) = all_24_0_28
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7823) all_24_0_28 = all_14_1_14
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2139) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (881), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3485) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3488) aNaturalNumber0(xm) = all_16_0_16
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7829) all_16_0_16 = all_14_1_14
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1292,7829) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1218) all_14_1_14 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1218,7829) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3488) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1123), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1228) and (2055) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2058) aNaturalNumber0(xn) = all_20_1_23
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7837) all_20_1_23 = all_14_2_15
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1228) and (2058) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (880), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2962) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2965) aNaturalNumber0(xm) = all_47_2_83
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7843) all_47_2_83 = all_14_1_14
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2965) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (879), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1294) and (2275) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2278) aNaturalNumber0(xm) = all_77_2_105
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7849) all_77_2_105 = all_14_1_14
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1294,7849) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1218) all_14_1_14 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1218,7849) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1294) all_77_2_105 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1109), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (1953) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1956) aNaturalNumber0(xn) = all_77_2_105
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7856) all_77_2_105 = all_14_2_15
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1294,7856) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1200) all_14_2_15 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1200,7856) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (367), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2498) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1775) and (1780) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7863) all_22_2_27 = all_20_0_22
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1788,7863) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1828) all_20_0_22 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2501) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (574), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3339) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3342) aNaturalNumber0(xp) = all_77_2_105
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7870) all_77_2_105 = all_67_3_98
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,7870) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1241) all_67_3_98 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1241,7870) yields a new equation:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3342) follows:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (303), into two cases.
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7874)  ~ (doDivides0(xp, all_0_3_3) = all_39_3_69)
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.04  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1313) and (7874) follows:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7875)  ~ (doDivides0(xp, all_0_3_3) = 0)
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (70) and (7875) yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7877) doDivides0(xp, all_0_3_3) = all_39_3_69
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1313) all_39_3_69 = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1313) and (7877) follows:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (70) doDivides0(xp, all_0_3_3) = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating formula (20) with all_642_0_217, all_0_3_3, xp and discharging atoms sdtlseqdt0(xp, all_0_3_3) = all_642_0_217, yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7880) all_642_0_217 = 0 | all_0_3_3 = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating formula (93) with xp, all_249_2_193, xp and discharging atoms sdtasdt0(xp, all_249_2_193) = xp, yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7881)  ? [v0] :  ? [v1] :  ? [v2] : (sdtasdt0(all_249_2_193, xp) = v2 & aNaturalNumber0(all_249_2_193) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = xp))
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating formula (13) with xn, all_32_2_48, all_0_3_3 and discharging atoms sdtpldt0(all_0_3_3, all_32_2_48) = xn, yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7882)  ? [v0] :  ? [v1] :  ? [v2] : (sdtpldt0(all_32_2_48, all_0_3_3) = v2 & aNaturalNumber0(all_32_2_48) = v1 & aNaturalNumber0(all_0_3_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = xn))
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating formula (34) with all_226_1_142, xp, xn and discharging atoms sdtpldt0(xn, xp) = all_226_1_142, yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7883)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_226_1_142) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating (7883) with all_6251_0_556, all_6251_1_557, all_6251_2_558 yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7884) aNaturalNumber0(all_226_1_142) = all_6251_0_556 & aNaturalNumber0(xp) = all_6251_1_557 & aNaturalNumber0(xn) = all_6251_2_558 & ( ~ (all_6251_1_557 = 0) |  ~ (all_6251_2_558 = 0) | all_6251_0_556 = 0)
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Applying alpha-rule on (7884) yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7885) aNaturalNumber0(all_226_1_142) = all_6251_0_556
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7886) aNaturalNumber0(xp) = all_6251_1_557
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7887) aNaturalNumber0(xn) = all_6251_2_558
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7888)  ~ (all_6251_1_557 = 0) |  ~ (all_6251_2_558 = 0) | all_6251_0_556 = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (7880), into two cases.
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1901) all_0_3_3 = sz00
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Equations (1901) can reduce 1898 to:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (197) $false
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1898)  ~ (all_0_3_3 = sz00)
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7892) all_642_0_217 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (7892), into two cases.
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7893) all_642_0_217 = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Equations (7893) can reduce 1849 to:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (197) $false
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1849)  ~ (all_642_0_217 = 0)
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7896)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating (7882) with all_6291_0_565, all_6291_1_566, all_6291_2_567 yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7897) sdtpldt0(all_32_2_48, all_0_3_3) = all_6291_0_565 & aNaturalNumber0(all_32_2_48) = all_6291_1_566 & aNaturalNumber0(all_0_3_3) = all_6291_2_567 & ( ~ (all_6291_1_566 = 0) |  ~ (all_6291_2_567 = 0) | all_6291_0_565 = xn)
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Applying alpha-rule on (7897) yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7898) sdtpldt0(all_32_2_48, all_0_3_3) = all_6291_0_565
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7899) aNaturalNumber0(all_32_2_48) = all_6291_1_566
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7900) aNaturalNumber0(all_0_3_3) = all_6291_2_567
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7901)  ~ (all_6291_1_566 = 0) |  ~ (all_6291_2_567 = 0) | all_6291_0_565 = xn
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with all_0_3_3, all_6291_2_567, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_6291_2_567, aNaturalNumber0(all_0_3_3) = 0, yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7902) all_6291_2_567 = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with xp, all_6251_1_557, 0 and discharging atoms aNaturalNumber0(xp) = all_6251_1_557, aNaturalNumber0(xp) = 0, yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7903) all_6251_1_557 = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (7902) and (7900) follows:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1775) aNaturalNumber0(all_0_3_3) = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (7903) and (7886) follows:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating (7881) with all_6319_0_571, all_6319_1_572, all_6319_2_573 yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7906) sdtasdt0(all_249_2_193, xp) = all_6319_0_571 & aNaturalNumber0(all_249_2_193) = all_6319_1_572 & aNaturalNumber0(xp) = all_6319_2_573 & ( ~ (all_6319_1_572 = 0) |  ~ (all_6319_2_573 = 0) | all_6319_0_571 = xp)
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Applying alpha-rule on (7906) yields:
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7907) sdtasdt0(all_249_2_193, xp) = all_6319_0_571
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7908) aNaturalNumber0(all_249_2_193) = all_6319_1_572
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7909) aNaturalNumber0(xp) = all_6319_2_573
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7910)  ~ (all_6319_1_572 = 0) |  ~ (all_6319_2_573 = 0) | all_6319_0_571 = xp
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.05  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating (7896) with all_6383_0_587, all_6383_1_588, all_6383_2_589 yields:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7911) doDivides0(xp, all_0_3_3) = all_6383_0_587 & aNaturalNumber0(all_0_3_3) = all_6383_1_588 & aNaturalNumber0(xp) = all_6383_2_589 & ( ~ (all_6383_0_587 = 0) |  ~ (all_6383_1_588 = 0) |  ~ (all_6383_2_589 = 0))
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Applying alpha-rule on (7911) yields:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7912) doDivides0(xp, all_0_3_3) = all_6383_0_587
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7913) aNaturalNumber0(all_0_3_3) = all_6383_1_588
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7914) aNaturalNumber0(xp) = all_6383_2_589
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7915)  ~ (all_6383_0_587 = 0) |  ~ (all_6383_1_588 = 0) |  ~ (all_6383_2_589 = 0)
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (79) with xp, all_0_3_3, all_6383_0_587, 0 and discharging atoms doDivides0(xp, all_0_3_3) = all_6383_0_587, doDivides0(xp, all_0_3_3) = 0, yields:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7916) all_6383_0_587 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with all_0_3_3, all_6383_1_588, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_6383_1_588, aNaturalNumber0(all_0_3_3) = 0, yields:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7917) all_6383_1_588 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with xp, all_6383_2_589, 0 and discharging atoms aNaturalNumber0(xp) = all_6383_2_589, aNaturalNumber0(xp) = 0, yields:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7918) all_6383_2_589 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with xp, all_6319_2_573, all_6383_2_589 and discharging atoms aNaturalNumber0(xp) = all_6383_2_589, aNaturalNumber0(xp) = all_6319_2_573, yields:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7919) all_6383_2_589 = all_6319_2_573
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (7918,7919) yields a new equation:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7920) all_6319_2_573 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (7920,7919) yields a new equation:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7918) all_6383_2_589 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (7915), into two cases.
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7922)  ~ (all_6383_0_587 = 0)
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Equations (7916) can reduce 7922 to:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (197) $false
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7916) all_6383_0_587 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7925)  ~ (all_6383_1_588 = 0) |  ~ (all_6383_2_589 = 0)
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (7925), into two cases.
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7926)  ~ (all_6383_1_588 = 0)
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Equations (7917) can reduce 7926 to:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (197) $false
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7917) all_6383_1_588 = 0
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7929)  ~ (all_6383_2_589 = 0)
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Equations (7918) can reduce 7929 to:
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (197) $false
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 222.83/172.06  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 222.91/172.14  																																																																																			|-Branch two:
% 222.91/172.14  																																																																																			| (7931)  ~ (xr = xk)
% 222.91/172.14  																																																																																			| (7932)  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(xk, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 222.91/172.14  																																																																																			|
% 222.91/172.14  																																																																																				| Instantiating (7932) with all_1006_0_606, all_1006_1_607, all_1006_2_608 yields:
% 222.91/172.14  																																																																																				| (7933) sdtlseqdt0(xk, xr) = all_1006_0_606 & aNaturalNumber0(xr) = all_1006_2_608 & aNaturalNumber0(xk) = all_1006_1_607 & ( ~ (all_1006_0_606 = 0) |  ~ (all_1006_1_607 = 0) |  ~ (all_1006_2_608 = 0))
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																				| Applying alpha-rule on (7933) yields:
% 222.91/172.14  																																																																																				| (7934) sdtlseqdt0(xk, xr) = all_1006_0_606
% 222.91/172.14  																																																																																				| (7935) aNaturalNumber0(xr) = all_1006_2_608
% 222.91/172.14  																																																																																				| (7936) aNaturalNumber0(xk) = all_1006_1_607
% 222.91/172.14  																																																																																				| (7937)  ~ (all_1006_0_606 = 0) |  ~ (all_1006_1_607 = 0) |  ~ (all_1006_2_608 = 0)
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																				| Instantiating formula (28) with xr, all_1006_2_608, 0 and discharging atoms aNaturalNumber0(xr) = all_1006_2_608, aNaturalNumber0(xr) = 0, yields:
% 222.91/172.14  																																																																																				| (7938) all_1006_2_608 = 0
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																				| Instantiating formula (28) with xk, all_1006_1_607, 0 and discharging atoms aNaturalNumber0(xk) = all_1006_1_607, aNaturalNumber0(xk) = 0, yields:
% 222.91/172.14  																																																																																				| (7939) all_1006_1_607 = 0
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																				| From (7938) and (7935) follows:
% 222.91/172.14  																																																																																				| (88) aNaturalNumber0(xr) = 0
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																				| From (7939) and (7936) follows:
% 222.91/172.14  																																																																																				| (1665) aNaturalNumber0(xk) = 0
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																				+-Applying beta-rule and splitting (342), into two cases.
% 222.91/172.14  																																																																																				|-Branch one:
% 222.91/172.14  																																																																																				| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																					| From (1790) and (1939) follows:
% 222.91/172.14  																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.14  																																																																																					|
% 222.91/172.14  																																																																																					| Using (12) and (1940) yields:
% 222.91/172.14  																																																																																					| (1311) $false
% 222.91/172.14  																																																																																					|
% 222.91/172.14  																																																																																					|-The branch is then unsatisfiable
% 222.91/172.14  																																																																																				|-Branch two:
% 222.91/172.14  																																																																																				| (1942) aNaturalNumber0(xm) = all_62_2_94
% 222.91/172.14  																																																																																				| (1790) all_62_2_94 = 0
% 222.91/172.14  																																																																																				|
% 222.91/172.14  																																																																																					| From (1790) and (1942) follows:
% 222.91/172.14  																																																																																					| (12) aNaturalNumber0(xm) = 0
% 222.91/172.14  																																																																																					|
% 222.91/172.15  																																																																																					+-Applying beta-rule and splitting (828), into two cases.
% 222.91/172.15  																																																																																					|-Branch one:
% 222.91/172.15  																																																																																					| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 222.91/172.15  																																																																																					|
% 222.91/172.15  																																																																																						| From (1227) and (1933) follows:
% 222.91/172.15  																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.15  																																																																																						|
% 222.91/172.15  																																																																																						| Using (91) and (1934) yields:
% 222.91/172.15  																																																																																						| (1311) $false
% 222.91/172.15  																																																																																						|
% 222.91/172.15  																																																																																						|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																					|-Branch two:
% 222.91/172.15  																																																																																					| (1936) aNaturalNumber0(xn) = all_18_1_20
% 222.91/172.15  																																																																																					| (1227) all_18_1_20 = 0
% 222.91/172.15  																																																																																					|
% 222.91/172.15  																																																																																						| From (1227) and (1936) follows:
% 222.91/172.15  																																																																																						| (91) aNaturalNumber0(xn) = 0
% 222.91/172.15  																																																																																						|
% 222.91/172.15  																																																																																						+-Applying beta-rule and splitting (1035), into two cases.
% 222.91/172.15  																																																																																						|-Branch one:
% 222.91/172.15  																																																																																						| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 222.91/172.15  																																																																																						|
% 222.91/172.15  																																																																																							| From (1294) and (1953) follows:
% 222.91/172.15  																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																							| Using (91) and (1934) yields:
% 222.91/172.15  																																																																																							| (1311) $false
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																							|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																						|-Branch two:
% 222.91/172.15  																																																																																						| (1956) aNaturalNumber0(xn) = all_77_2_105
% 222.91/172.15  																																																																																						| (1957) all_77_2_105 = all_37_4_65
% 222.91/172.15  																																																																																						|
% 222.91/172.15  																																																																																							| Combining equations (1294,1957) yields a new equation:
% 222.91/172.15  																																																																																							| (1232) all_37_4_65 = 0
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																							| Combining equations (1232,1957) yields a new equation:
% 222.91/172.15  																																																																																							| (1294) all_77_2_105 = 0
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																							| From (1294) and (1956) follows:
% 222.91/172.15  																																																																																							| (91) aNaturalNumber0(xn) = 0
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																							+-Applying beta-rule and splitting (876), into two cases.
% 222.91/172.15  																																																																																							|-Branch one:
% 222.91/172.15  																																																																																							| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																								| From (1789) and (1945) follows:
% 222.91/172.15  																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																								| Using (12) and (1940) yields:
% 222.91/172.15  																																																																																								| (1311) $false
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																								|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																							|-Branch two:
% 222.91/172.15  																																																																																							| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.91/172.15  																																																																																							| (1949) all_57_2_90 = all_14_1_14
% 222.91/172.15  																																																																																							|
% 222.91/172.15  																																																																																								| Combining equations (1789,1949) yields a new equation:
% 222.91/172.15  																																																																																								| (1218) all_14_1_14 = 0
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																								| Combining equations (1218,1949) yields a new equation:
% 222.91/172.15  																																																																																								| (1789) all_57_2_90 = 0
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																								| From (1789) and (1948) follows:
% 222.91/172.15  																																																																																								| (12) aNaturalNumber0(xm) = 0
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																								+-Applying beta-rule and splitting (808), into two cases.
% 222.91/172.15  																																																																																								|-Branch one:
% 222.91/172.15  																																																																																								| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																									| From (1281) and (1969) follows:
% 222.91/172.15  																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																									| Using (12) and (1940) yields:
% 222.91/172.15  																																																																																									| (1311) $false
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																									|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																								|-Branch two:
% 222.91/172.15  																																																																																								| (1972) aNaturalNumber0(xm) = all_12_0_10
% 222.91/172.15  																																																																																								| (1973) all_22_1_26 = all_12_0_10
% 222.91/172.15  																																																																																								|
% 222.91/172.15  																																																																																									| Combining equations (1973,1229) yields a new equation:
% 222.91/172.15  																																																																																									| (2959) all_12_0_10 = 0
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																									| Simplifying 2959 yields:
% 222.91/172.15  																																																																																									| (1281) all_12_0_10 = 0
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																									| From (1281) and (1972) follows:
% 222.91/172.15  																																																																																									| (12) aNaturalNumber0(xm) = 0
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																									+-Applying beta-rule and splitting (976), into two cases.
% 222.91/172.15  																																																																																									|-Branch one:
% 222.91/172.15  																																																																																									| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																										| From (1227) and (1933) follows:
% 222.91/172.15  																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																										| Using (91) and (1934) yields:
% 222.91/172.15  																																																																																										| (1311) $false
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																										|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																									|-Branch two:
% 222.91/172.15  																																																																																									| (1936) aNaturalNumber0(xn) = all_18_1_20
% 222.91/172.15  																																																																																									| (1965) all_62_1_93 = all_18_1_20
% 222.91/172.15  																																																																																									|
% 222.91/172.15  																																																																																										| Combining equations (1240,1965) yields a new equation:
% 222.91/172.15  																																																																																										| (1227) all_18_1_20 = 0
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																										| Combining equations (1227,1965) yields a new equation:
% 222.91/172.15  																																																																																										| (1240) all_62_1_93 = 0
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																										| From (1227) and (1936) follows:
% 222.91/172.15  																																																																																										| (91) aNaturalNumber0(xn) = 0
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																										+-Applying beta-rule and splitting (989), into two cases.
% 222.91/172.15  																																																																																										|-Branch one:
% 222.91/172.15  																																																																																										| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																											| From (1350) and (1985) follows:
% 222.91/172.15  																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																											| Using (91) and (1934) yields:
% 222.91/172.15  																																																																																											| (1311) $false
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																											|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																										|-Branch two:
% 222.91/172.15  																																																																																										| (1988) aNaturalNumber0(xn) = all_24_0_28
% 222.91/172.15  																																																																																										| (1989) all_57_1_89 = all_24_0_28
% 222.91/172.15  																																																																																										|
% 222.91/172.15  																																																																																											| Combining equations (980,1989) yields a new equation:
% 222.91/172.15  																																																																																											| (1350) all_24_0_28 = 0
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																											| Combining equations (1350,1989) yields a new equation:
% 222.91/172.15  																																																																																											| (980) all_57_1_89 = 0
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																											| From (1350) and (1988) follows:
% 222.91/172.15  																																																																																											| (91) aNaturalNumber0(xn) = 0
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																											+-Applying beta-rule and splitting (874), into two cases.
% 222.91/172.15  																																																																																											|-Branch one:
% 222.91/172.15  																																																																																											| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																												| From (1791) and (1977) follows:
% 222.91/172.15  																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																												| Using (12) and (1940) yields:
% 222.91/172.15  																																																																																												| (1311) $false
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																												|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																											|-Branch two:
% 222.91/172.15  																																																																																											| (1980) aNaturalNumber0(xm) = all_72_2_101
% 222.91/172.15  																																																																																											| (1981) all_72_2_101 = all_14_1_14
% 222.91/172.15  																																																																																											|
% 222.91/172.15  																																																																																												| Combining equations (1791,1981) yields a new equation:
% 222.91/172.15  																																																																																												| (1218) all_14_1_14 = 0
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																												| Combining equations (1218,1981) yields a new equation:
% 222.91/172.15  																																																																																												| (1791) all_72_2_101 = 0
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																												| From (1791) and (1980) follows:
% 222.91/172.15  																																																																																												| (12) aNaturalNumber0(xm) = 0
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																												+-Applying beta-rule and splitting (964), into two cases.
% 222.91/172.15  																																																																																												|-Branch one:
% 222.91/172.15  																																																																																												| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																													| From (1350) and (1985) follows:
% 222.91/172.15  																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																													| Using (91) and (1934) yields:
% 222.91/172.15  																																																																																													| (1311) $false
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																													|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																												|-Branch two:
% 222.91/172.15  																																																																																												| (1988) aNaturalNumber0(xn) = all_24_0_28
% 222.91/172.15  																																																																																												| (2003) all_62_1_93 = all_24_0_28
% 222.91/172.15  																																																																																												|
% 222.91/172.15  																																																																																													| Combining equations (1240,2003) yields a new equation:
% 222.91/172.15  																																																																																													| (1350) all_24_0_28 = 0
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																													| Combining equations (1350,2003) yields a new equation:
% 222.91/172.15  																																																																																													| (1240) all_62_1_93 = 0
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																													| From (1350) and (1988) follows:
% 222.91/172.15  																																																																																													| (91) aNaturalNumber0(xn) = 0
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																													+-Applying beta-rule and splitting (319), into two cases.
% 222.91/172.15  																																																																																													|-Branch one:
% 222.91/172.15  																																																																																													| (1993)  ~ (aNaturalNumber0(sz10) = all_67_2_97)
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																														| From (1829) and (1993) follows:
% 222.91/172.15  																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.91/172.15  																																																																																														|
% 222.91/172.15  																																																																																														| Using (61) and (1994) yields:
% 222.91/172.15  																																																																																														| (1311) $false
% 222.91/172.15  																																																																																														|
% 222.91/172.15  																																																																																														|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																													|-Branch two:
% 222.91/172.15  																																																																																													| (1996) aNaturalNumber0(sz10) = all_67_2_97
% 222.91/172.15  																																																																																													| (1829) all_67_2_97 = 0
% 222.91/172.15  																																																																																													|
% 222.91/172.15  																																																																																														| From (1829) and (1996) follows:
% 222.91/172.15  																																																																																														| (61) aNaturalNumber0(sz10) = 0
% 222.91/172.15  																																																																																														|
% 222.91/172.15  																																																																																														+-Applying beta-rule and splitting (897), into two cases.
% 222.91/172.15  																																																																																														|-Branch one:
% 222.91/172.15  																																																																																														| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 222.91/172.15  																																																																																														|
% 222.91/172.15  																																																																																															| From (1789) and (1945) follows:
% 222.91/172.15  																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																															| Using (12) and (1940) yields:
% 222.91/172.15  																																																																																															| (1311) $false
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																															|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																														|-Branch two:
% 222.91/172.15  																																																																																														| (1948) aNaturalNumber0(xm) = all_57_2_90
% 222.91/172.15  																																																																																														| (2019) all_57_2_90 = all_12_1_11
% 222.91/172.15  																																																																																														|
% 222.91/172.15  																																																																																															| Combining equations (1789,2019) yields a new equation:
% 222.91/172.15  																																																																																															| (1221) all_12_1_11 = 0
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																															| Combining equations (1221,2019) yields a new equation:
% 222.91/172.15  																																																																																															| (1789) all_57_2_90 = 0
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																															| From (1789) and (1948) follows:
% 222.91/172.15  																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																															+-Applying beta-rule and splitting (578), into two cases.
% 222.91/172.15  																																																																																															|-Branch one:
% 222.91/172.15  																																																																																															| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																																| From (1283) and (2007) follows:
% 222.91/172.15  																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																| Using (9) and (2008) yields:
% 222.91/172.15  																																																																																																| (1311) $false
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																															|-Branch two:
% 222.91/172.15  																																																																																															| (2010) aNaturalNumber0(xp) = all_26_2_33
% 222.91/172.15  																																																																																															| (2011) all_67_3_98 = all_26_2_33
% 222.91/172.15  																																																																																															|
% 222.91/172.15  																																																																																																| Combining equations (1241,2011) yields a new equation:
% 222.91/172.15  																																																																																																| (1283) all_26_2_33 = 0
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																| Combining equations (1283,2011) yields a new equation:
% 222.91/172.15  																																																																																																| (1241) all_67_3_98 = 0
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																| From (1283) and (2010) follows:
% 222.91/172.15  																																																																																																| (9) aNaturalNumber0(xp) = 0
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																+-Applying beta-rule and splitting (557), into two cases.
% 222.91/172.15  																																																																																																|-Branch one:
% 222.91/172.15  																																																																																																| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																	| From (1787) and (2031) follows:
% 222.91/172.15  																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																	| Using (9) and (2008) yields:
% 222.91/172.15  																																																																																																	| (1311) $false
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																	|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																																|-Branch two:
% 222.91/172.15  																																																																																																| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.91/172.15  																																																																																																| (2035) all_72_3_102 = all_20_2_24
% 222.91/172.15  																																																																																																|
% 222.91/172.15  																																																																																																	| Combining equations (1243,2035) yields a new equation:
% 222.91/172.15  																																																																																																	| (1787) all_20_2_24 = 0
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																	| Combining equations (1787,2035) yields a new equation:
% 222.91/172.15  																																																																																																	| (1243) all_72_3_102 = 0
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																	| From (1787) and (2034) follows:
% 222.91/172.15  																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																	+-Applying beta-rule and splitting (544), into two cases.
% 222.91/172.15  																																																																																																	|-Branch one:
% 222.91/172.15  																																																																																																	| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																		| From (1292) and (2023) follows:
% 222.91/172.15  																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																		| Using (9) and (2008) yields:
% 222.91/172.15  																																																																																																		| (1311) $false
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																		|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																																	|-Branch two:
% 222.91/172.15  																																																																																																	| (2026) aNaturalNumber0(xp) = all_16_0_16
% 222.91/172.15  																																																																																																	| (2027) all_77_3_106 = all_16_0_16
% 222.91/172.15  																																																																																																	|
% 222.91/172.15  																																																																																																		| Combining equations (1245,2027) yields a new equation:
% 222.91/172.15  																																																																																																		| (1292) all_16_0_16 = 0
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																		| Combining equations (1292,2027) yields a new equation:
% 222.91/172.15  																																																																																																		| (1245) all_77_3_106 = 0
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																		| From (1292) and (2026) follows:
% 222.91/172.15  																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																		+-Applying beta-rule and splitting (644), into two cases.
% 222.91/172.15  																																																																																																		|-Branch one:
% 222.91/172.15  																																																																																																		| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																			| From (1281) and (2039) follows:
% 222.91/172.15  																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																			| Using (9) and (2008) yields:
% 222.91/172.15  																																																																																																			| (1311) $false
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																			|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																																		|-Branch two:
% 222.91/172.15  																																																																																																		| (2042) aNaturalNumber0(xp) = all_12_0_10
% 222.91/172.15  																																																																																																		| (2051) all_39_6_72 = all_12_0_10
% 222.91/172.15  																																																																																																		|
% 222.91/172.15  																																																																																																			| Combining equations (2051,629) yields a new equation:
% 222.91/172.15  																																																																																																			| (2959) all_12_0_10 = 0
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																			| Simplifying 2959 yields:
% 222.91/172.15  																																																																																																			| (1281) all_12_0_10 = 0
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																			| From (1281) and (2042) follows:
% 222.91/172.15  																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																			+-Applying beta-rule and splitting (677), into two cases.
% 222.91/172.15  																																																																																																			|-Branch one:
% 222.91/172.15  																																																																																																			| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																				| From (1281) and (2039) follows:
% 222.91/172.15  																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.15  																																																																																																				|
% 222.91/172.15  																																																																																																				| Using (9) and (2008) yields:
% 222.91/172.15  																																																																																																				| (1311) $false
% 222.91/172.15  																																																																																																				|
% 222.91/172.15  																																																																																																				|-The branch is then unsatisfiable
% 222.91/172.15  																																																																																																			|-Branch two:
% 222.91/172.15  																																																																																																			| (2042) aNaturalNumber0(xp) = all_12_0_10
% 222.91/172.15  																																																																																																			| (2043) all_26_1_32 = all_12_0_10
% 222.91/172.15  																																																																																																			|
% 222.91/172.15  																																																																																																				| Combining equations (1202,2043) yields a new equation:
% 222.91/172.15  																																																																																																				| (1281) all_12_0_10 = 0
% 222.91/172.15  																																																																																																				|
% 222.91/172.16  																																																																																																				| Combining equations (1281,2043) yields a new equation:
% 222.91/172.16  																																																																																																				| (1202) all_26_1_32 = 0
% 222.91/172.16  																																																																																																				|
% 222.91/172.16  																																																																																																				| From (1281) and (2042) follows:
% 222.91/172.16  																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.91/172.16  																																																																																																				|
% 222.91/172.16  																																																																																																				+-Applying beta-rule and splitting (938), into two cases.
% 222.91/172.16  																																																																																																				|-Branch one:
% 222.91/172.16  																																																																																																				| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 222.91/172.16  																																																																																																				|
% 222.91/172.16  																																																																																																					| From (1293) and (2061) follows:
% 222.91/172.16  																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																					| Using (91) and (1934) yields:
% 222.91/172.16  																																																																																																					| (1311) $false
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																					|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																				|-Branch two:
% 222.91/172.16  																																																																																																				| (2064) aNaturalNumber0(xn) = all_47_2_83
% 222.91/172.16  																																																																																																				| (2065) all_77_1_104 = all_47_2_83
% 222.91/172.16  																																																																																																				|
% 222.91/172.16  																																																																																																					| Combining equations (1246,2065) yields a new equation:
% 222.91/172.16  																																																																																																					| (1293) all_47_2_83 = 0
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																					| Combining equations (1293,2065) yields a new equation:
% 222.91/172.16  																																																																																																					| (1246) all_77_1_104 = 0
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																					| From (1293) and (2064) follows:
% 222.91/172.16  																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																					+-Applying beta-rule and splitting (811), into two cases.
% 222.91/172.16  																																																																																																					|-Branch one:
% 222.91/172.16  																																																																																																					| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																						| From (1228) and (2055) follows:
% 222.91/172.16  																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.16  																																																																																																						|
% 222.91/172.16  																																																																																																						| Using (91) and (1934) yields:
% 222.91/172.16  																																																																																																						| (1311) $false
% 222.91/172.16  																																																																																																						|
% 222.91/172.16  																																																																																																						|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																					|-Branch two:
% 222.91/172.16  																																																																																																					| (2058) aNaturalNumber0(xn) = all_20_1_23
% 222.91/172.16  																																																																																																					| (1228) all_20_1_23 = 0
% 222.91/172.16  																																																																																																					|
% 222.91/172.16  																																																																																																						| From (1228) and (2058) follows:
% 222.91/172.16  																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 222.91/172.16  																																																																																																						|
% 222.91/172.16  																																																																																																						+-Applying beta-rule and splitting (752), into two cases.
% 222.91/172.16  																																																																																																						|-Branch one:
% 222.91/172.16  																																																																																																						| (2075)  ~ (aNaturalNumber0(sz10) = all_39_7_73)
% 222.91/172.16  																																																																																																						|
% 222.91/172.16  																																																																																																							| From (1236) and (2075) follows:
% 222.91/172.16  																																																																																																							| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.91/172.16  																																																																																																							|
% 222.91/172.16  																																																																																																							| Using (61) and (1994) yields:
% 222.91/172.16  																																																																																																							| (1311) $false
% 222.91/172.16  																																																																																																							|
% 222.91/172.16  																																																																																																							|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																						|-Branch two:
% 222.91/172.16  																																																																																																						| (2078) aNaturalNumber0(sz10) = all_39_7_73
% 222.91/172.16  																																																																																																						| (1236) all_39_7_73 = 0
% 222.91/172.16  																																																																																																						|
% 222.91/172.16  																																																																																																							| From (1236) and (2078) follows:
% 222.91/172.16  																																																																																																							| (61) aNaturalNumber0(sz10) = 0
% 222.91/172.16  																																																																																																							|
% 222.91/172.16  																																																																																																							+-Applying beta-rule and splitting (414), into two cases.
% 222.91/172.16  																																																																																																							|-Branch one:
% 222.91/172.16  																																																																																																							| (2069)  ~ (aNaturalNumber0(sz00) = all_16_0_16)
% 222.91/172.16  																																																																																																							|
% 222.91/172.16  																																																																																																								| From (1292) and (2069) follows:
% 222.91/172.16  																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.91/172.16  																																																																																																								|
% 222.91/172.16  																																																																																																								| Using (26) and (2070) yields:
% 222.91/172.16  																																																																																																								| (1311) $false
% 222.91/172.16  																																																																																																								|
% 222.91/172.16  																																																																																																								|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																							|-Branch two:
% 222.91/172.16  																																																																																																							| (2072) aNaturalNumber0(sz00) = all_16_0_16
% 222.91/172.16  																																																																																																							| (1292) all_16_0_16 = 0
% 222.91/172.16  																																																																																																							|
% 222.91/172.16  																																																																																																								| From (1292) and (2072) follows:
% 222.91/172.16  																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 222.91/172.16  																																																																																																								|
% 222.91/172.16  																																																																																																								+-Applying beta-rule and splitting (498), into two cases.
% 222.91/172.16  																																																																																																								|-Branch one:
% 222.91/172.16  																																																																																																								| (2089)  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 222.91/172.16  																																																																																																								|
% 222.91/172.16  																																																																																																									| From (1292) and (2089) follows:
% 222.91/172.16  																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																									| Using (1284) and (2090) yields:
% 222.91/172.16  																																																																																																									| (1311) $false
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																									|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																								|-Branch two:
% 222.91/172.16  																																																																																																								| (2092) aNaturalNumber0(all_0_9_9) = all_16_0_16
% 222.91/172.16  																																																																																																								| (2093) all_16_0_16 = all_12_0_10
% 222.91/172.16  																																																																																																								|
% 222.91/172.16  																																																																																																									| Combining equations (1292,2093) yields a new equation:
% 222.91/172.16  																																																																																																									| (1281) all_12_0_10 = 0
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																									| Combining equations (1281,2093) yields a new equation:
% 222.91/172.16  																																																																																																									| (1292) all_16_0_16 = 0
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																									| From (1292) and (2092) follows:
% 222.91/172.16  																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																									+-Applying beta-rule and splitting (1029), into two cases.
% 222.91/172.16  																																																																																																									|-Branch one:
% 222.91/172.16  																																																																																																									| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																										| From (1221) and (2081) follows:
% 222.91/172.16  																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																										| Using (91) and (1934) yields:
% 222.91/172.16  																																																																																																										| (1311) $false
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																										|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																									|-Branch two:
% 222.91/172.16  																																																																																																									| (2084) aNaturalNumber0(xn) = all_12_1_11
% 222.91/172.16  																																																																																																									| (2085) all_39_8_74 = all_12_1_11
% 222.91/172.16  																																																																																																									|
% 222.91/172.16  																																																																																																										| Combining equations (1179,2085) yields a new equation:
% 222.91/172.16  																																																																																																										| (1221) all_12_1_11 = 0
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																										| Combining equations (1221,2085) yields a new equation:
% 222.91/172.16  																																																																																																										| (1179) all_39_8_74 = 0
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																										| From (1221) and (2084) follows:
% 222.91/172.16  																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																										+-Applying beta-rule and splitting (540), into two cases.
% 222.91/172.16  																																																																																																										|-Branch one:
% 222.91/172.16  																																																																																																										| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																											| From (1788) and (2105) follows:
% 222.91/172.16  																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.16  																																																																																																											|
% 222.91/172.16  																																																																																																											| Using (9) and (2008) yields:
% 222.91/172.16  																																																																																																											| (1311) $false
% 222.91/172.16  																																																																																																											|
% 222.91/172.16  																																																																																																											|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																										|-Branch two:
% 222.91/172.16  																																																																																																										| (2108) aNaturalNumber0(xp) = all_22_2_27
% 222.91/172.16  																																																																																																										| (2109) all_77_3_106 = all_22_2_27
% 222.91/172.16  																																																																																																										|
% 222.91/172.16  																																																																																																											| Combining equations (1245,2109) yields a new equation:
% 222.91/172.16  																																																																																																											| (1788) all_22_2_27 = 0
% 222.91/172.16  																																																																																																											|
% 222.91/172.16  																																																																																																											| From (1788) and (2108) follows:
% 222.91/172.16  																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 222.91/172.16  																																																																																																											|
% 222.91/172.16  																																																																																																											+-Applying beta-rule and splitting (892), into two cases.
% 222.91/172.16  																																																																																																											|-Branch one:
% 222.91/172.16  																																																																																																											| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 222.91/172.16  																																																																																																											|
% 222.91/172.16  																																																																																																												| From (1830) and (2097) follows:
% 222.91/172.16  																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																												| Using (12) and (1940) yields:
% 222.91/172.16  																																																																																																												| (1311) $false
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																												|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																											|-Branch two:
% 222.91/172.16  																																																																																																											| (2100) aNaturalNumber0(xm) = all_82_2_109
% 222.91/172.16  																																																																																																											| (2101) all_82_2_109 = all_12_1_11
% 222.91/172.16  																																																																																																											|
% 222.91/172.16  																																																																																																												| Combining equations (1830,2101) yields a new equation:
% 222.91/172.16  																																																																																																												| (1221) all_12_1_11 = 0
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																												| Combining equations (1221,2101) yields a new equation:
% 222.91/172.16  																																																																																																												| (1830) all_82_2_109 = 0
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																												| From (1830) and (2100) follows:
% 222.91/172.16  																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																												+-Applying beta-rule and splitting (1107), into two cases.
% 222.91/172.16  																																																																																																												|-Branch one:
% 222.91/172.16  																																																																																																												| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																													| From (1829) and (2120) follows:
% 222.91/172.16  																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																													| Using (91) and (1934) yields:
% 222.91/172.16  																																																																																																													| (1311) $false
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																													|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																												|-Branch two:
% 222.91/172.16  																																																																																																												| (2123) aNaturalNumber0(xn) = all_67_2_97
% 222.91/172.16  																																																																																																												| (2124) all_67_2_97 = all_14_2_15
% 222.91/172.16  																																																																																																												|
% 222.91/172.16  																																																																																																													| Combining equations (1829,2124) yields a new equation:
% 222.91/172.16  																																																																																																													| (1200) all_14_2_15 = 0
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																													| Combining equations (1200,2124) yields a new equation:
% 222.91/172.16  																																																																																																													| (1829) all_67_2_97 = 0
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																													| From (1829) and (2123) follows:
% 222.91/172.16  																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																													+-Applying beta-rule and splitting (534), into two cases.
% 222.91/172.16  																																																																																																													|-Branch one:
% 222.91/172.16  																																																																																																													| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																														| From (1830) and (2112) follows:
% 222.91/172.16  																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																														| Using (9) and (2008) yields:
% 222.91/172.16  																																																																																																														| (1311) $false
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																														|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																													|-Branch two:
% 222.91/172.16  																																																																																																													| (2115) aNaturalNumber0(xp) = all_82_2_109
% 222.91/172.16  																																																																																																													| (2116) all_82_2_109 = all_77_3_106
% 222.91/172.16  																																																																																																													|
% 222.91/172.16  																																																																																																														| Combining equations (1830,2116) yields a new equation:
% 222.91/172.16  																																																																																																														| (1245) all_77_3_106 = 0
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																														| Combining equations (1245,2116) yields a new equation:
% 222.91/172.16  																																																																																																														| (1830) all_82_2_109 = 0
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																														| From (1830) and (2115) follows:
% 222.91/172.16  																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																														+-Applying beta-rule and splitting (842), into two cases.
% 222.91/172.16  																																																																																																														|-Branch one:
% 222.91/172.16  																																																																																																														| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																															| From (1350) and (2136) follows:
% 222.91/172.16  																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																															| Using (12) and (1940) yields:
% 222.91/172.16  																																																																																																															| (1311) $false
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																															|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																														|-Branch two:
% 222.91/172.16  																																																																																																														| (2139) aNaturalNumber0(xm) = all_24_0_28
% 222.91/172.16  																																																																																																														| (2140) all_24_0_28 = all_18_1_20
% 222.91/172.16  																																																																																																														|
% 222.91/172.16  																																																																																																															| Combining equations (2140,1350) yields a new equation:
% 222.91/172.16  																																																																																																															| (4545) all_18_1_20 = 0
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																															| Simplifying 4545 yields:
% 222.91/172.16  																																																																																																															| (1227) all_18_1_20 = 0
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																															| From (1350) and (2139) follows:
% 222.91/172.16  																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																															+-Applying beta-rule and splitting (388), into two cases.
% 222.91/172.16  																																																																																																															|-Branch one:
% 222.91/172.16  																																																																																																															| (2128)  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																																| From (1828) and (2128) follows:
% 222.91/172.16  																																																																																																																| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																| Using (1295) and (2129) yields:
% 222.91/172.16  																																																																																																																| (1311) $false
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																															|-Branch two:
% 222.91/172.16  																																																																																																															| (2131) aNaturalNumber0(all_0_7_7) = all_20_0_22
% 222.91/172.16  																																																																																																															| (2132) all_77_2_105 = all_20_0_22
% 222.91/172.16  																																																																																																															|
% 222.91/172.16  																																																																																																																| Combining equations (1294,2132) yields a new equation:
% 222.91/172.16  																																																																																																																| (1828) all_20_0_22 = 0
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																| Combining equations (1828,2132) yields a new equation:
% 222.91/172.16  																																																																																																																| (1294) all_77_2_105 = 0
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																| From (1828) and (2131) follows:
% 222.91/172.16  																																																																																																																| (1295) aNaturalNumber0(all_0_7_7) = 0
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																+-Applying beta-rule and splitting (1106), into two cases.
% 222.91/172.16  																																																																																																																|-Branch one:
% 222.91/172.16  																																																																																																																| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																	| From (1830) and (2151) follows:
% 222.91/172.16  																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																	| Using (91) and (1934) yields:
% 222.91/172.16  																																																																																																																	| (1311) $false
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																	|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																																|-Branch two:
% 222.91/172.16  																																																																																																																| (2154) aNaturalNumber0(xn) = all_82_2_109
% 222.91/172.16  																																																																																																																| (2155) all_82_2_109 = all_14_2_15
% 222.91/172.16  																																																																																																																|
% 222.91/172.16  																																																																																																																	| Combining equations (1830,2155) yields a new equation:
% 222.91/172.16  																																																																																																																	| (1200) all_14_2_15 = 0
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																	| Combining equations (1200,2155) yields a new equation:
% 222.91/172.16  																																																																																																																	| (1830) all_82_2_109 = 0
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																	| From (1830) and (2154) follows:
% 222.91/172.16  																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																	+-Applying beta-rule and splitting (801), into two cases.
% 222.91/172.16  																																																																																																																	|-Branch one:
% 222.91/172.16  																																																																																																																	| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																		| From (1788) and (2144) follows:
% 222.91/172.16  																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.91/172.16  																																																																																																																		|
% 222.91/172.16  																																																																																																																		| Using (12) and (1940) yields:
% 222.91/172.16  																																																																																																																		| (1311) $false
% 222.91/172.16  																																																																																																																		|
% 222.91/172.16  																																																																																																																		|-The branch is then unsatisfiable
% 222.91/172.16  																																																																																																																	|-Branch two:
% 222.91/172.16  																																																																																																																	| (2147) aNaturalNumber0(xm) = all_22_2_27
% 222.91/172.16  																																																																																																																	| (2148) all_22_1_26 = all_22_2_27
% 222.91/172.16  																																																																																																																	|
% 222.91/172.16  																																																																																																																		| Combining equations (2148,1229) yields a new equation:
% 222.91/172.16  																																																																																																																		| (5091) all_22_2_27 = 0
% 222.91/172.16  																																																																																																																		|
% 222.91/172.16  																																																																																																																		| Simplifying 5091 yields:
% 222.91/172.16  																																																																																																																		| (1788) all_22_2_27 = 0
% 222.91/172.16  																																																																																																																		|
% 222.91/172.16  																																																																																																																		| From (1788) and (2147) follows:
% 222.91/172.17  																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 222.91/172.17  																																																																																																																		|
% 222.91/172.17  																																																																																																																		+-Applying beta-rule and splitting (813), into two cases.
% 222.91/172.17  																																																																																																																		|-Branch one:
% 222.91/172.17  																																																																																																																		| (2165)  ~ (aNaturalNumber0(sz00) = all_20_1_23)
% 222.91/172.17  																																																																																																																		|
% 222.91/172.17  																																																																																																																			| From (1228) and (2165) follows:
% 222.91/172.17  																																																																																																																			| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.91/172.17  																																																																																																																			|
% 222.91/172.17  																																																																																																																			| Using (26) and (2070) yields:
% 222.91/172.17  																																																																																																																			| (1311) $false
% 222.91/172.17  																																																																																																																			|
% 222.91/172.17  																																																																																																																			|-The branch is then unsatisfiable
% 222.91/172.17  																																																																																																																		|-Branch two:
% 222.91/172.17  																																																																																																																		| (2168) aNaturalNumber0(sz00) = all_20_1_23
% 222.91/172.17  																																																																																																																		| (1228) all_20_1_23 = 0
% 222.91/172.17  																																																																																																																		|
% 222.91/172.17  																																																																																																																			| From (1228) and (2168) follows:
% 222.91/172.17  																																																																																																																			| (26) aNaturalNumber0(sz00) = 0
% 222.91/172.17  																																																																																																																			|
% 222.91/172.17  																																																																																																																			+-Applying beta-rule and splitting (395), into two cases.
% 222.91/172.17  																																																																																																																			|-Branch one:
% 222.91/172.17  																																																																																																																			| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 222.91/172.17  																																																																																																																			|
% 222.91/172.17  																																																																																																																				| From (1293) and (2159) follows:
% 222.91/172.17  																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.91/172.17  																																																																																																																				|
% 222.91/172.17  																																																																																																																				| Using (9) and (2008) yields:
% 222.91/172.17  																																																																																																																				| (1311) $false
% 222.91/172.17  																																																																																																																				|
% 222.91/172.17  																																																																																																																				|-The branch is then unsatisfiable
% 222.91/172.17  																																																																																																																			|-Branch two:
% 222.91/172.17  																																																																																																																			| (2162) aNaturalNumber0(xp) = all_47_2_83
% 222.91/172.17  																																																																																																																			| (1293) all_47_2_83 = 0
% 222.91/172.17  																																																																																																																			|
% 222.91/172.17  																																																																																																																				| From (1293) and (2162) follows:
% 222.91/172.17  																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 222.91/172.17  																																																																																																																				|
% 222.91/172.17  																																																																																																																				+-Applying beta-rule and splitting (470), into two cases.
% 222.91/172.17  																																																																																																																				|-Branch one:
% 222.91/172.17  																																																																																																																				| (2178)  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 222.91/172.17  																																																																																																																				|
% 222.91/172.17  																																																																																																																					| From (1828) and (2178) follows:
% 222.91/172.17  																																																																																																																					| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.91/172.17  																																																																																																																					|
% 222.91/172.17  																																																																																																																					| Using (1284) and (2090) yields:
% 222.91/172.17  																																																																																																																					| (1311) $false
% 222.91/172.17  																																																																																																																					|
% 222.91/172.17  																																																																																																																					|-The branch is then unsatisfiable
% 222.91/172.17  																																																																																																																				|-Branch two:
% 222.91/172.17  																																																																																																																				| (2181) aNaturalNumber0(all_0_9_9) = all_20_0_22
% 222.91/172.17  																																																																																																																				| (2182) all_24_2_30 = all_20_0_22
% 222.91/172.17  																																																																																																																				|
% 222.99/172.17  																																																																																																																					| Combining equations (1282,2182) yields a new equation:
% 222.99/172.17  																																																																																																																					| (1828) all_20_0_22 = 0
% 222.99/172.17  																																																																																																																					|
% 222.99/172.17  																																																																																																																					| Combining equations (1828,2182) yields a new equation:
% 222.99/172.17  																																																																																																																					| (1282) all_24_2_30 = 0
% 222.99/172.17  																																																																																																																					|
% 222.99/172.17  																																																																																																																					| From (1828) and (2181) follows:
% 222.99/172.17  																																																																																																																					| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.99/172.17  																																																																																																																					|
% 222.99/172.17  																																																																																																																					+-Applying beta-rule and splitting (647), into two cases.
% 222.99/172.17  																																																																																																																					|-Branch one:
% 222.99/172.17  																																																																																																																					| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 222.99/172.17  																																																																																																																					|
% 222.99/172.17  																																																																																																																						| From (1828) and (2171) follows:
% 222.99/172.17  																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.99/172.17  																																																																																																																						|
% 222.99/172.17  																																																																																																																						| Using (9) and (2008) yields:
% 222.99/172.17  																																																																																																																						| (1311) $false
% 222.99/172.17  																																																																																																																						|
% 222.99/172.17  																																																																																																																						|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																					|-Branch two:
% 222.99/172.17  																																																																																																																					| (2174) aNaturalNumber0(xp) = all_20_0_22
% 222.99/172.17  																																																																																																																					| (2175) all_37_2_63 = all_20_0_22
% 222.99/172.17  																																																																																																																					|
% 222.99/172.17  																																																																																																																						| Combining equations (1195,2175) yields a new equation:
% 222.99/172.17  																																																																																																																						| (1828) all_20_0_22 = 0
% 222.99/172.17  																																																																																																																						|
% 222.99/172.17  																																																																																																																						| From (1828) and (2174) follows:
% 222.99/172.17  																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 222.99/172.17  																																																																																																																						|
% 222.99/172.17  																																																																																																																						+-Applying beta-rule and splitting (587), into two cases.
% 222.99/172.17  																																																																																																																						|-Branch one:
% 222.99/172.17  																																																																																																																						| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 222.99/172.17  																																																																																																																						|
% 222.99/172.17  																																																																																																																							| From (1789) and (2186) follows:
% 222.99/172.17  																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																							| Using (9) and (2008) yields:
% 222.99/172.17  																																																																																																																							| (1311) $false
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																							|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																						|-Branch two:
% 222.99/172.17  																																																																																																																						| (2189) aNaturalNumber0(xp) = all_57_2_90
% 222.99/172.17  																																																																																																																						| (2198) all_57_2_90 = all_57_3_91
% 222.99/172.17  																																																																																																																						|
% 222.99/172.17  																																																																																																																							| Combining equations (1789,2198) yields a new equation:
% 222.99/172.17  																																																																																																																							| (2199) all_57_3_91 = 0
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																							| Combining equations (2199,2198) yields a new equation:
% 222.99/172.17  																																																																																																																							| (1789) all_57_2_90 = 0
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																							| From (1789) and (2189) follows:
% 222.99/172.17  																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																							+-Applying beta-rule and splitting (618), into two cases.
% 222.99/172.17  																																																																																																																							|-Branch one:
% 222.99/172.17  																																																																																																																							| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																								| From (1789) and (2186) follows:
% 222.99/172.17  																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																								| Using (9) and (2008) yields:
% 222.99/172.17  																																																																																																																								| (1311) $false
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																								|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																							|-Branch two:
% 222.99/172.17  																																																																																																																							| (2189) aNaturalNumber0(xp) = all_57_2_90
% 222.99/172.17  																																																																																																																							| (2190) all_57_2_90 = all_47_3_84
% 222.99/172.17  																																																																																																																							|
% 222.99/172.17  																																																																																																																								| Combining equations (1789,2190) yields a new equation:
% 222.99/172.17  																																																																																																																								| (2191) all_47_3_84 = 0
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																								| Combining equations (2191,2190) yields a new equation:
% 222.99/172.17  																																																																																																																								| (1789) all_57_2_90 = 0
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																								| From (1789) and (2189) follows:
% 222.99/172.17  																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																								+-Applying beta-rule and splitting (1114), into two cases.
% 222.99/172.17  																																																																																																																								|-Branch one:
% 222.99/172.17  																																																																																																																								| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																									| From (1282) and (2210) follows:
% 222.99/172.17  																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																									| Using (91) and (1934) yields:
% 222.99/172.17  																																																																																																																									| (1311) $false
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																									|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																								|-Branch two:
% 222.99/172.17  																																																																																																																								| (2213) aNaturalNumber0(xn) = all_24_2_30
% 222.99/172.17  																																																																																																																								| (2214) all_24_2_30 = all_14_2_15
% 222.99/172.17  																																																																																																																								|
% 222.99/172.17  																																																																																																																									| Combining equations (1282,2214) yields a new equation:
% 222.99/172.17  																																																																																																																									| (1200) all_14_2_15 = 0
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																									| Combining equations (1200,2214) yields a new equation:
% 222.99/172.17  																																																																																																																									| (1282) all_24_2_30 = 0
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																									| From (1282) and (2213) follows:
% 222.99/172.17  																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																									+-Applying beta-rule and splitting (509), into two cases.
% 222.99/172.17  																																																																																																																									|-Branch one:
% 222.99/172.17  																																																																																																																									| (2202)  ~ (aNaturalNumber0(xk) = all_57_2_90)
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																										| From (1789) and (2202) follows:
% 222.99/172.17  																																																																																																																										| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																										| Using (1665) and (1670) yields:
% 222.99/172.17  																																																																																																																										| (1311) $false
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																										|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																									|-Branch two:
% 222.99/172.17  																																																																																																																									| (2205) aNaturalNumber0(xk) = all_57_2_90
% 222.99/172.17  																																																																																																																									| (2206) all_57_2_90 = all_52_2_87
% 222.99/172.17  																																																																																																																									|
% 222.99/172.17  																																																																																																																										| Combining equations (1789,2206) yields a new equation:
% 222.99/172.17  																																																																																																																										| (1674) all_52_2_87 = 0
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																										| Combining equations (1674,2206) yields a new equation:
% 222.99/172.17  																																																																																																																										| (1789) all_57_2_90 = 0
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																										| From (1789) and (2205) follows:
% 222.99/172.17  																																																																																																																										| (1665) aNaturalNumber0(xk) = 0
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																										+-Applying beta-rule and splitting (481), into two cases.
% 222.99/172.17  																																																																																																																										|-Branch one:
% 222.99/172.17  																																																																																																																										| (2226)  ~ (aNaturalNumber0(xr) = all_12_0_10)
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																											| From (1281) and (2226) follows:
% 222.99/172.17  																																																																																																																											| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 222.99/172.17  																																																																																																																											|
% 222.99/172.17  																																																																																																																											| Using (88) and (8229) yields:
% 222.99/172.17  																																																																																																																											| (1311) $false
% 222.99/172.17  																																																																																																																											|
% 222.99/172.17  																																																																																																																											|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																										|-Branch two:
% 222.99/172.17  																																																																																																																										| (2229) aNaturalNumber0(xr) = all_12_0_10
% 222.99/172.17  																																																																																																																										| (1281) all_12_0_10 = 0
% 222.99/172.17  																																																																																																																										|
% 222.99/172.17  																																																																																																																											| From (1281) and (2229) follows:
% 222.99/172.17  																																																																																																																											| (88) aNaturalNumber0(xr) = 0
% 222.99/172.17  																																																																																																																											|
% 222.99/172.17  																																																																																																																											+-Applying beta-rule and splitting (495), into two cases.
% 222.99/172.17  																																																																																																																											|-Branch one:
% 222.99/172.17  																																																																																																																											| (2218)  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 222.99/172.17  																																																																																																																											|
% 222.99/172.17  																																																																																																																												| From (1787) and (2218) follows:
% 222.99/172.17  																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.99/172.17  																																																																																																																												|
% 222.99/172.17  																																																																																																																												| Using (1284) and (2090) yields:
% 222.99/172.17  																																																																																																																												| (1311) $false
% 222.99/172.17  																																																																																																																												|
% 222.99/172.17  																																																																																																																												|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																											|-Branch two:
% 222.99/172.17  																																																																																																																											| (2221) aNaturalNumber0(all_0_9_9) = all_20_2_24
% 222.99/172.17  																																																																																																																											| (2222) all_20_2_24 = all_12_0_10
% 222.99/172.17  																																																																																																																											|
% 222.99/172.17  																																																																																																																												| From (1787) and (2221) follows:
% 222.99/172.17  																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.99/172.17  																																																																																																																												|
% 222.99/172.17  																																																																																																																												+-Applying beta-rule and splitting (812), into two cases.
% 222.99/172.17  																																																																																																																												|-Branch one:
% 222.99/172.17  																																																																																																																												| (2240)  ~ (aNaturalNumber0(sz10) = all_20_1_23)
% 222.99/172.17  																																																																																																																												|
% 222.99/172.17  																																																																																																																													| From (1228) and (2240) follows:
% 222.99/172.17  																																																																																																																													| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 222.99/172.17  																																																																																																																													|
% 222.99/172.17  																																																																																																																													| Using (61) and (1994) yields:
% 222.99/172.17  																																																																																																																													| (1311) $false
% 222.99/172.17  																																																																																																																													|
% 222.99/172.17  																																																																																																																													|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																												|-Branch two:
% 222.99/172.17  																																																																																																																												| (2243) aNaturalNumber0(sz10) = all_20_1_23
% 222.99/172.17  																																																																																																																												| (1228) all_20_1_23 = 0
% 222.99/172.17  																																																																																																																												|
% 222.99/172.17  																																																																																																																													| From (1228) and (2243) follows:
% 222.99/172.17  																																																																																																																													| (61) aNaturalNumber0(sz10) = 0
% 222.99/172.17  																																																																																																																													|
% 222.99/172.17  																																																																																																																													+-Applying beta-rule and splitting (479), into two cases.
% 222.99/172.17  																																																																																																																													|-Branch one:
% 222.99/172.17  																																																																																																																													| (2232)  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 222.99/172.17  																																																																																																																													|
% 222.99/172.17  																																																																																																																														| From (1350) and (2232) follows:
% 222.99/172.17  																																																																																																																														| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																														| Using (1284) and (2090) yields:
% 222.99/172.17  																																																																																																																														| (1311) $false
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																														|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																													|-Branch two:
% 222.99/172.17  																																																																																																																													| (2235) aNaturalNumber0(all_0_9_9) = all_24_0_28
% 222.99/172.17  																																																																																																																													| (2236) all_24_0_28 = all_24_2_30
% 222.99/172.17  																																																																																																																													|
% 222.99/172.17  																																																																																																																														| Combining equations (2236,1350) yields a new equation:
% 222.99/172.17  																																																																																																																														| (5099) all_24_2_30 = 0
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																														| Simplifying 5099 yields:
% 222.99/172.17  																																																																																																																														| (1282) all_24_2_30 = 0
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																														| From (1350) and (2235) follows:
% 222.99/172.17  																																																																																																																														| (1284) aNaturalNumber0(all_0_9_9) = 0
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																														+-Applying beta-rule and splitting (1063), into two cases.
% 222.99/172.17  																																																																																																																														|-Branch one:
% 222.99/172.17  																																																																																																																														| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																															| From (1283) and (2252) follows:
% 222.99/172.17  																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.99/172.17  																																																																																																																															|
% 222.99/172.17  																																																																																																																															| Using (91) and (1934) yields:
% 222.99/172.17  																																																																																																																															| (1311) $false
% 222.99/172.17  																																																																																																																															|
% 222.99/172.17  																																																																																																																															|-The branch is then unsatisfiable
% 222.99/172.17  																																																																																																																														|-Branch two:
% 222.99/172.17  																																																																																																																														| (2255) aNaturalNumber0(xn) = all_26_2_33
% 222.99/172.17  																																																																																																																														| (2256) all_26_2_33 = all_18_2_21
% 222.99/172.17  																																																																																																																														|
% 222.99/172.17  																																																																																																																															| Combining equations (1283,2256) yields a new equation:
% 222.99/172.17  																																																																																																																															| (1226) all_18_2_21 = 0
% 222.99/172.17  																																																																																																																															|
% 222.99/172.17  																																																																																																																															| Combining equations (1226,2256) yields a new equation:
% 222.99/172.17  																																																																																																																															| (1283) all_26_2_33 = 0
% 222.99/172.17  																																																																																																																															|
% 222.99/172.17  																																																																																																																															| From (1283) and (2255) follows:
% 222.99/172.17  																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 222.99/172.17  																																																																																																																															|
% 222.99/172.17  																																																																																																																															+-Applying beta-rule and splitting (344), into two cases.
% 222.99/172.17  																																																																																																																															|-Branch one:
% 222.99/172.17  																																																																																																																															| (2246)  ~ (aNaturalNumber0(sz00) = all_62_2_94)
% 222.99/172.17  																																																																																																																															|
% 222.99/172.17  																																																																																																																																| From (1790) and (2246) follows:
% 222.99/172.17  																																																																																																																																| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 222.99/172.17  																																																																																																																																|
% 222.99/172.17  																																																																																																																																| Using (26) and (2070) yields:
% 222.99/172.18  																																																																																																																																| (1311) $false
% 222.99/172.18  																																																																																																																																|
% 222.99/172.18  																																																																																																																																|-The branch is then unsatisfiable
% 222.99/172.18  																																																																																																																															|-Branch two:
% 222.99/172.18  																																																																																																																															| (2249) aNaturalNumber0(sz00) = all_62_2_94
% 222.99/172.18  																																																																																																																															| (1790) all_62_2_94 = 0
% 222.99/172.18  																																																																																																																															|
% 222.99/172.18  																																																																																																																																| From (1790) and (2249) follows:
% 222.99/172.18  																																																																																																																																| (26) aNaturalNumber0(sz00) = 0
% 222.99/172.18  																																																																																																																																|
% 222.99/172.18  																																																																																																																																+-Applying beta-rule and splitting (1027), into two cases.
% 222.99/172.18  																																																																																																																																|-Branch one:
% 222.99/172.18  																																																																																																																																| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 222.99/172.18  																																																																																																																																|
% 222.99/172.18  																																																																																																																																	| From (848) and (2268) follows:
% 222.99/172.18  																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 222.99/172.18  																																																																																																																																	|
% 222.99/172.18  																																																																																																																																	| Using (91) and (1934) yields:
% 222.99/172.18  																																																																																																																																	| (1311) $false
% 222.99/172.18  																																																																																																																																	|
% 222.99/172.18  																																																																																																																																	|-The branch is then unsatisfiable
% 222.99/172.18  																																																																																																																																|-Branch two:
% 222.99/172.18  																																																																																																																																| (2271) aNaturalNumber0(xn) = all_16_1_17
% 222.99/172.18  																																																																																																																																| (2272) all_39_8_74 = all_16_1_17
% 222.99/172.18  																																																																																																																																|
% 222.99/172.18  																																																																																																																																	| Combining equations (1179,2272) yields a new equation:
% 222.99/172.18  																																																																																																																																	| (848) all_16_1_17 = 0
% 222.99/172.18  																																																																																																																																	|
% 222.99/172.18  																																																																																																																																	| From (848) and (2271) follows:
% 222.99/172.18  																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 222.99/172.18  																																																																																																																																	|
% 222.99/172.18  																																																																																																																																	+-Applying beta-rule and splitting (529), into two cases.
% 222.99/172.18  																																																																																																																																	|-Branch one:
% 222.99/172.18  																																																																																																																																	| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 222.99/172.18  																																																																																																																																	|
% 222.99/172.18  																																																																																																																																		| From (1292) and (2023) follows:
% 222.99/172.18  																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																		| Using (9) and (2008) yields:
% 222.99/172.18  																																																																																																																																		| (1311) $false
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																		|-The branch is then unsatisfiable
% 222.99/172.18  																																																																																																																																	|-Branch two:
% 222.99/172.18  																																																																																																																																	| (2026) aNaturalNumber0(xp) = all_16_0_16
% 222.99/172.18  																																																																																																																																	| (2264) all_82_3_110 = all_16_0_16
% 222.99/172.18  																																																																																																																																	|
% 222.99/172.18  																																																																																																																																		| Combining equations (1247,2264) yields a new equation:
% 222.99/172.18  																																																																																																																																		| (1292) all_16_0_16 = 0
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																		| Combining equations (1292,2264) yields a new equation:
% 222.99/172.18  																																																																																																																																		| (1247) all_82_3_110 = 0
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																		| From (1292) and (2026) follows:
% 222.99/172.18  																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																		+-Applying beta-rule and splitting (686), into two cases.
% 222.99/172.18  																																																																																																																																		|-Branch one:
% 222.99/172.18  																																																																																																																																		| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																			| From (1787) and (2031) follows:
% 222.99/172.18  																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 222.99/172.18  																																																																																																																																			|
% 222.99/172.18  																																																																																																																																			| Using (9) and (2008) yields:
% 222.99/172.18  																																																																																																																																			| (1311) $false
% 222.99/172.18  																																																																																																																																			|
% 222.99/172.18  																																																																																																																																			|-The branch is then unsatisfiable
% 222.99/172.18  																																																																																																																																		|-Branch two:
% 222.99/172.18  																																																																																																																																		| (2034) aNaturalNumber0(xp) = all_20_2_24
% 222.99/172.18  																																																																																																																																		| (2287) all_24_1_29 = all_20_2_24
% 222.99/172.18  																																																																																																																																		|
% 222.99/172.18  																																																																																																																																			| Combining equations (1207,2287) yields a new equation:
% 222.99/172.18  																																																																																																																																			| (1787) all_20_2_24 = 0
% 222.99/172.18  																																																																																																																																			|
% 222.99/172.18  																																																																																																																																			| From (1787) and (2034) follows:
% 222.99/172.18  																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 222.99/172.18  																																																																																																																																			|
% 222.99/172.18  																																																																																																																																			+-Applying beta-rule and splitting (822), into two cases.
% 222.99/172.18  																																																																																																																																			|-Branch one:
% 222.99/172.18  																																																																																																																																			| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 222.99/172.18  																																																																																																																																			|
% 222.99/172.18  																																																																																																																																				| From (1294) and (2275) follows:
% 222.99/172.18  																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 222.99/172.18  																																																																																																																																				|
% 222.99/172.18  																																																																																																																																				| Using (12) and (1940) yields:
% 222.99/172.18  																																																																																																																																				| (1311) $false
% 222.99/172.18  																																																																																																																																				|
% 222.99/172.18  																																																																																																																																				|-The branch is then unsatisfiable
% 222.99/172.18  																																																																																																																																			|-Branch two:
% 222.99/172.18  																																																																																																																																			| (2278) aNaturalNumber0(xm) = all_77_2_105
% 222.99/172.18  																																																																																																																																			| (2279) all_77_2_105 = all_20_1_23
% 222.99/172.18  																																																																																																																																			|
% 222.99/172.18  																																																																																																																																				| Combining equations (1294,2279) yields a new equation:
% 222.99/172.18  																																																																																																																																				| (1228) all_20_1_23 = 0
% 222.99/172.18  																																																																																																																																				|
% 222.99/172.18  																																																																																																																																				| Combining equations (1228,2279) yields a new equation:
% 222.99/172.18  																																																																																																																																				| (1294) all_77_2_105 = 0
% 223.00/172.18  																																																																																																																																				|
% 223.00/172.18  																																																																																																																																				| From (1294) and (2278) follows:
% 223.00/172.18  																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.00/172.18  																																																																																																																																				|
% 223.00/172.18  																																																																																																																																				+-Applying beta-rule and splitting (756), into two cases.
% 223.00/172.18  																																																																																																																																				|-Branch one:
% 223.00/172.18  																																																																																																																																				| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.00/172.18  																																																																																																																																				|
% 223.00/172.18  																																																																																																																																					| From (1828) and (2298) follows:
% 223.00/172.18  																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																					| Using (12) and (1940) yields:
% 223.00/172.18  																																																																																																																																					| (1311) $false
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																					|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																				|-Branch two:
% 223.00/172.18  																																																																																																																																				| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.00/172.18  																																																																																																																																				| (2302) all_39_7_73 = all_20_0_22
% 223.00/172.18  																																																																																																																																				|
% 223.00/172.18  																																																																																																																																					| Combining equations (1236,2302) yields a new equation:
% 223.00/172.18  																																																																																																																																					| (1828) all_20_0_22 = 0
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																					| Combining equations (1828,2302) yields a new equation:
% 223.00/172.18  																																																																																																																																					| (1236) all_39_7_73 = 0
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																					| From (1828) and (2301) follows:
% 223.00/172.18  																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																					+-Applying beta-rule and splitting (449), into two cases.
% 223.00/172.18  																																																																																																																																					|-Branch one:
% 223.00/172.18  																																																																																																																																					| (2290)  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																						| From (1830) and (2290) follows:
% 223.00/172.18  																																																																																																																																						| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																						| Using (1284) and (2090) yields:
% 223.00/172.18  																																																																																																																																						| (1311) $false
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																						|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																					|-Branch two:
% 223.00/172.18  																																																																																																																																					| (2293) aNaturalNumber0(all_0_9_9) = all_82_2_109
% 223.00/172.18  																																																																																																																																					| (2294) all_82_2_109 = all_26_2_33
% 223.00/172.18  																																																																																																																																					|
% 223.00/172.18  																																																																																																																																						| Combining equations (1830,2294) yields a new equation:
% 223.00/172.18  																																																																																																																																						| (1283) all_26_2_33 = 0
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																						| Combining equations (1283,2294) yields a new equation:
% 223.00/172.18  																																																																																																																																						| (1830) all_82_2_109 = 0
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																						| From (1830) and (2293) follows:
% 223.00/172.18  																																																																																																																																						| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																						+-Applying beta-rule and splitting (455), into two cases.
% 223.00/172.18  																																																																																																																																						|-Branch one:
% 223.00/172.18  																																																																																																																																						| (2312)  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																							| From (1788) and (2312) follows:
% 223.00/172.18  																																																																																																																																							| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																							| Using (1284) and (2090) yields:
% 223.00/172.18  																																																																																																																																							| (1311) $false
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																							|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																						|-Branch two:
% 223.00/172.18  																																																																																																																																						| (2315) aNaturalNumber0(all_0_9_9) = all_22_2_27
% 223.00/172.18  																																																																																																																																						| (2316) all_26_2_33 = all_22_2_27
% 223.00/172.18  																																																																																																																																						|
% 223.00/172.18  																																																																																																																																							| Combining equations (1283,2316) yields a new equation:
% 223.00/172.18  																																																																																																																																							| (1788) all_22_2_27 = 0
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																							| Combining equations (1788,2316) yields a new equation:
% 223.00/172.18  																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																							| From (1788) and (2315) follows:
% 223.00/172.18  																																																																																																																																							| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																							+-Applying beta-rule and splitting (313), into two cases.
% 223.00/172.18  																																																																																																																																							|-Branch one:
% 223.00/172.18  																																																																																																																																							| (2306)  ~ (aNaturalNumber0(sz00) = all_82_2_109)
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																								| From (1830) and (2306) follows:
% 223.00/172.18  																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.00/172.18  																																																																																																																																								|
% 223.00/172.18  																																																																																																																																								| Using (26) and (2070) yields:
% 223.00/172.18  																																																																																																																																								| (1311) $false
% 223.00/172.18  																																																																																																																																								|
% 223.00/172.18  																																																																																																																																								|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																							|-Branch two:
% 223.00/172.18  																																																																																																																																							| (2309) aNaturalNumber0(sz00) = all_82_2_109
% 223.00/172.18  																																																																																																																																							| (1830) all_82_2_109 = 0
% 223.00/172.18  																																																																																																																																							|
% 223.00/172.18  																																																																																																																																								| From (1830) and (2309) follows:
% 223.00/172.18  																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 223.00/172.18  																																																																																																																																								|
% 223.00/172.18  																																																																																																																																								+-Applying beta-rule and splitting (496), into two cases.
% 223.00/172.18  																																																																																																																																								|-Branch one:
% 223.00/172.18  																																																																																																																																								| (2326)  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 223.00/172.18  																																																																																																																																								|
% 223.00/172.18  																																																																																																																																									| From (1294) and (2326) follows:
% 223.00/172.18  																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																									| Using (1284) and (2090) yields:
% 223.00/172.18  																																																																																																																																									| (1311) $false
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																									|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																								|-Branch two:
% 223.00/172.18  																																																																																																																																								| (2329) aNaturalNumber0(all_0_9_9) = all_77_2_105
% 223.00/172.18  																																																																																																																																								| (2330) all_77_2_105 = all_12_0_10
% 223.00/172.18  																																																																																																																																								|
% 223.00/172.18  																																																																																																																																									| Combining equations (1294,2330) yields a new equation:
% 223.00/172.18  																																																																																																																																									| (1281) all_12_0_10 = 0
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																									| Combining equations (1281,2330) yields a new equation:
% 223.00/172.18  																																																																																																																																									| (1294) all_77_2_105 = 0
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																									| From (1294) and (2329) follows:
% 223.00/172.18  																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																									+-Applying beta-rule and splitting (933), into two cases.
% 223.00/172.18  																																																																																																																																									|-Branch one:
% 223.00/172.18  																																																																																																																																									| (2320)  ~ (aNaturalNumber0(sz00) = all_77_1_104)
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																										| From (1246) and (2320) follows:
% 223.00/172.18  																																																																																																																																										| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.00/172.18  																																																																																																																																										|
% 223.00/172.18  																																																																																																																																										| Using (26) and (2070) yields:
% 223.00/172.18  																																																																																																																																										| (1311) $false
% 223.00/172.18  																																																																																																																																										|
% 223.00/172.18  																																																																																																																																										|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																									|-Branch two:
% 223.00/172.18  																																																																																																																																									| (2323) aNaturalNumber0(sz00) = all_77_1_104
% 223.00/172.18  																																																																																																																																									| (1246) all_77_1_104 = 0
% 223.00/172.18  																																																																																																																																									|
% 223.00/172.18  																																																																																																																																										| From (1246) and (2323) follows:
% 223.00/172.18  																																																																																																																																										| (26) aNaturalNumber0(sz00) = 0
% 223.00/172.18  																																																																																																																																										|
% 223.00/172.18  																																																																																																																																										+-Applying beta-rule and splitting (1009), into two cases.
% 223.00/172.18  																																																																																																																																										|-Branch one:
% 223.00/172.18  																																																																																																																																										| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.00/172.18  																																																																																																																																										|
% 223.00/172.18  																																																																																																																																											| From (1829) and (2120) follows:
% 223.00/172.18  																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																											| Using (91) and (1934) yields:
% 223.00/172.18  																																																																																																																																											| (1311) $false
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																											|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																										|-Branch two:
% 223.00/172.18  																																																																																																																																										| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.00/172.18  																																																																																																																																										| (2346) all_67_2_97 = all_39_8_74
% 223.00/172.18  																																																																																																																																										|
% 223.00/172.18  																																																																																																																																											| Combining equations (1829,2346) yields a new equation:
% 223.00/172.18  																																																																																																																																											| (1179) all_39_8_74 = 0
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																											| Combining equations (1179,2346) yields a new equation:
% 223.00/172.18  																																																																																																																																											| (1829) all_67_2_97 = 0
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																											| From (1829) and (2123) follows:
% 223.00/172.18  																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																											+-Applying beta-rule and splitting (1143), into two cases.
% 223.00/172.18  																																																																																																																																											|-Branch one:
% 223.00/172.18  																																																																																																																																											| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																												| From (1242) and (2334) follows:
% 223.00/172.18  																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																												| Using (91) and (1934) yields:
% 223.00/172.18  																																																																																																																																												| (1311) $false
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																												|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																											|-Branch two:
% 223.00/172.18  																																																																																																																																											| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.00/172.18  																																																																																																																																											| (2338) all_67_1_96 = all_12_2_12
% 223.00/172.18  																																																																																																																																											|
% 223.00/172.18  																																																																																																																																												| Combining equations (1242,2338) yields a new equation:
% 223.00/172.18  																																																																																																																																												| (1223) all_12_2_12 = 0
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																												| Combining equations (1223,2338) yields a new equation:
% 223.00/172.18  																																																																																																																																												| (1242) all_67_1_96 = 0
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																												| From (1242) and (2337) follows:
% 223.00/172.18  																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																												+-Applying beta-rule and splitting (1138), into two cases.
% 223.00/172.18  																																																																																																																																												|-Branch one:
% 223.00/172.18  																																																																																																																																												| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																													| From (1283) and (2252) follows:
% 223.00/172.18  																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.18  																																																																																																																																													|
% 223.00/172.18  																																																																																																																																													| Using (91) and (1934) yields:
% 223.00/172.18  																																																																																																																																													| (1311) $false
% 223.00/172.18  																																																																																																																																													|
% 223.00/172.18  																																																																																																																																													|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																												|-Branch two:
% 223.00/172.18  																																																																																																																																												| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.00/172.18  																																																																																																																																												| (2362) all_26_2_33 = all_12_2_12
% 223.00/172.18  																																																																																																																																												|
% 223.00/172.18  																																																																																																																																													| Combining equations (1283,2362) yields a new equation:
% 223.00/172.18  																																																																																																																																													| (1223) all_12_2_12 = 0
% 223.00/172.18  																																																																																																																																													|
% 223.00/172.18  																																																																																																																																													| Combining equations (1223,2362) yields a new equation:
% 223.00/172.18  																																																																																																																																													| (1283) all_26_2_33 = 0
% 223.00/172.18  																																																																																																																																													|
% 223.00/172.18  																																																																																																																																													| From (1283) and (2255) follows:
% 223.00/172.18  																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.00/172.18  																																																																																																																																													|
% 223.00/172.18  																																																																																																																																													+-Applying beta-rule and splitting (965), into two cases.
% 223.00/172.18  																																																																																																																																													|-Branch one:
% 223.00/172.18  																																																																																																																																													| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.00/172.18  																																																																																																																																													|
% 223.00/172.18  																																																																																																																																														| From (1283) and (2252) follows:
% 223.00/172.18  																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.18  																																																																																																																																														|
% 223.00/172.18  																																																																																																																																														| Using (91) and (1934) yields:
% 223.00/172.18  																																																																																																																																														| (1311) $false
% 223.00/172.18  																																																																																																																																														|
% 223.00/172.18  																																																																																																																																														|-The branch is then unsatisfiable
% 223.00/172.18  																																																																																																																																													|-Branch two:
% 223.00/172.19  																																																																																																																																													| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.00/172.19  																																																																																																																																													| (2354) all_62_1_93 = all_26_2_33
% 223.00/172.19  																																																																																																																																													|
% 223.00/172.19  																																																																																																																																														| Combining equations (1240,2354) yields a new equation:
% 223.00/172.19  																																																																																																																																														| (1283) all_26_2_33 = 0
% 223.00/172.19  																																																																																																																																														|
% 223.00/172.19  																																																																																																																																														| Combining equations (1283,2354) yields a new equation:
% 223.00/172.19  																																																																																																																																														| (1240) all_62_1_93 = 0
% 223.00/172.19  																																																																																																																																														|
% 223.00/172.19  																																																																																																																																														| From (1283) and (2255) follows:
% 223.00/172.19  																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.00/172.19  																																																																																																																																														|
% 223.00/172.19  																																																																																																																																														+-Applying beta-rule and splitting (919), into two cases.
% 223.00/172.19  																																																																																																																																														|-Branch one:
% 223.00/172.19  																																																																																																																																														| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.00/172.19  																																																																																																																																														|
% 223.00/172.19  																																																																																																																																															| From (1281) and (2374) follows:
% 223.00/172.19  																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																															| Using (91) and (1934) yields:
% 223.00/172.19  																																																																																																																																															| (1311) $false
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																															|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																														|-Branch two:
% 223.00/172.19  																																																																																																																																														| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.00/172.19  																																																																																																																																														| (2378) all_82_1_108 = all_12_0_10
% 223.00/172.19  																																																																																																																																														|
% 223.00/172.19  																																																																																																																																															| Combining equations (1249,2378) yields a new equation:
% 223.00/172.19  																																																																																																																																															| (1281) all_12_0_10 = 0
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																															| Combining equations (1281,2378) yields a new equation:
% 223.00/172.19  																																																																																																																																															| (1249) all_82_1_108 = 0
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																															| From (1281) and (2377) follows:
% 223.00/172.19  																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																															+-Applying beta-rule and splitting (704), into two cases.
% 223.00/172.19  																																																																																																																																															|-Branch one:
% 223.00/172.19  																																																																																																																																															| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																																| From (1787) and (2366) follows:
% 223.00/172.19  																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																| Using (12) and (1940) yields:
% 223.00/172.19  																																																																																																																																																| (1311) $false
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																															|-Branch two:
% 223.00/172.19  																																																																																																																																															| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.00/172.19  																																																																																																																																															| (2370) all_72_1_100 = all_20_2_24
% 223.00/172.19  																																																																																																																																															|
% 223.00/172.19  																																																																																																																																																| Combining equations (1244,2370) yields a new equation:
% 223.00/172.19  																																																																																																																																																| (1787) all_20_2_24 = 0
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																| Combining equations (1787,2370) yields a new equation:
% 223.00/172.19  																																																																																																																																																| (1244) all_72_1_100 = 0
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																| From (1787) and (2369) follows:
% 223.00/172.19  																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																+-Applying beta-rule and splitting (934), into two cases.
% 223.00/172.19  																																																																																																																																																|-Branch one:
% 223.00/172.19  																																																																																																																																																| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																	| From (1830) and (2151) follows:
% 223.00/172.19  																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																	| Using (91) and (1934) yields:
% 223.00/172.19  																																																																																																																																																	| (1311) $false
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																	|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																|-Branch two:
% 223.00/172.19  																																																																																																																																																| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.00/172.19  																																																																																																																																																| (2394) all_82_2_109 = all_77_1_104
% 223.00/172.19  																																																																																																																																																|
% 223.00/172.19  																																																																																																																																																	| Combining equations (1830,2394) yields a new equation:
% 223.00/172.19  																																																																																																																																																	| (1246) all_77_1_104 = 0
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																	| Combining equations (1246,2394) yields a new equation:
% 223.00/172.19  																																																																																																																																																	| (1830) all_82_2_109 = 0
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																	| From (1830) and (2154) follows:
% 223.00/172.19  																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																	+-Applying beta-rule and splitting (767), into two cases.
% 223.00/172.19  																																																																																																																																																	|-Branch one:
% 223.00/172.19  																																																																																																																																																	| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																		| From (1282) and (2382) follows:
% 223.00/172.19  																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																		| Using (12) and (1940) yields:
% 223.00/172.19  																																																																																																																																																		| (1311) $false
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																		|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																	|-Branch two:
% 223.00/172.19  																																																																																																																																																	| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.00/172.19  																																																																																																																																																	| (2386) all_39_7_73 = all_24_2_30
% 223.00/172.19  																																																																																																																																																	|
% 223.00/172.19  																																																																																																																																																		| Combining equations (1236,2386) yields a new equation:
% 223.00/172.19  																																																																																																																																																		| (1282) all_24_2_30 = 0
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																		| Combining equations (1282,2386) yields a new equation:
% 223.00/172.19  																																																																																																																																																		| (1236) all_39_7_73 = 0
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																		| From (1282) and (2385) follows:
% 223.00/172.19  																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																		+-Applying beta-rule and splitting (817), into two cases.
% 223.00/172.19  																																																																																																																																																		|-Branch one:
% 223.00/172.19  																																																																																																																																																		| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																			| From (1791) and (1977) follows:
% 223.00/172.19  																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																			| Using (12) and (1940) yields:
% 223.00/172.19  																																																																																																																																																			| (1311) $false
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																			|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																		|-Branch two:
% 223.00/172.19  																																																																																																																																																		| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.00/172.19  																																																																																																																																																		| (2408) all_72_2_101 = all_20_1_23
% 223.00/172.19  																																																																																																																																																		|
% 223.00/172.19  																																																																																																																																																			| Combining equations (1791,2408) yields a new equation:
% 223.00/172.19  																																																																																																																																																			| (1228) all_20_1_23 = 0
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																			| Combining equations (1228,2408) yields a new equation:
% 223.00/172.19  																																																																																																																																																			| (1791) all_72_2_101 = 0
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																			| From (1791) and (1980) follows:
% 223.00/172.19  																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																			+-Applying beta-rule and splitting (981), into two cases.
% 223.00/172.19  																																																																																																																																																			|-Branch one:
% 223.00/172.19  																																																																																																																																																			| (2398)  ~ (aNaturalNumber0(sz10) = all_57_1_89)
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																				| From (980) and (2398) follows:
% 223.00/172.19  																																																																																																																																																				| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.00/172.19  																																																																																																																																																				|
% 223.00/172.19  																																																																																																																																																				| Using (61) and (1994) yields:
% 223.00/172.19  																																																																																																																																																				| (1311) $false
% 223.00/172.19  																																																																																																																																																				|
% 223.00/172.19  																																																																																																																																																				|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																			|-Branch two:
% 223.00/172.19  																																																																																																																																																			| (2401) aNaturalNumber0(sz10) = all_57_1_89
% 223.00/172.19  																																																																																																																																																			| (980) all_57_1_89 = 0
% 223.00/172.19  																																																																																																																																																			|
% 223.00/172.19  																																																																																																																																																				| From (980) and (2401) follows:
% 223.00/172.19  																																																																																																																																																				| (61) aNaturalNumber0(sz10) = 0
% 223.00/172.19  																																																																																																																																																				|
% 223.00/172.19  																																																																																																																																																				+-Applying beta-rule and splitting (571), into two cases.
% 223.00/172.19  																																																																																																																																																				|-Branch one:
% 223.00/172.19  																																																																																																																																																				| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.00/172.19  																																																																																																																																																				|
% 223.00/172.19  																																																																																																																																																					| From (1789) and (2186) follows:
% 223.00/172.19  																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																					| Using (9) and (2008) yields:
% 223.00/172.19  																																																																																																																																																					| (1311) $false
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																					|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																				|-Branch two:
% 223.00/172.19  																																																																																																																																																				| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.00/172.19  																																																																																																																																																				| (2422) all_67_3_98 = all_57_2_90
% 223.00/172.19  																																																																																																																																																				|
% 223.00/172.19  																																																																																																																																																					| Combining equations (1241,2422) yields a new equation:
% 223.00/172.19  																																																																																																																																																					| (1789) all_57_2_90 = 0
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																					| Combining equations (1789,2422) yields a new equation:
% 223.00/172.19  																																																																																																																																																					| (1241) all_67_3_98 = 0
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																					| From (1789) and (2189) follows:
% 223.00/172.19  																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																					+-Applying beta-rule and splitting (829), into two cases.
% 223.00/172.19  																																																																																																																																																					|-Branch one:
% 223.00/172.19  																																																																																																																																																					| (2412)  ~ (aNaturalNumber0(sz10) = all_18_1_20)
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																						| From (1227) and (2412) follows:
% 223.00/172.19  																																																																																																																																																						| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.00/172.19  																																																																																																																																																						|
% 223.00/172.19  																																																																																																																																																						| Using (61) and (1994) yields:
% 223.00/172.19  																																																																																																																																																						| (1311) $false
% 223.00/172.19  																																																																																																																																																						|
% 223.00/172.19  																																																																																																																																																						|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																					|-Branch two:
% 223.00/172.19  																																																																																																																																																					| (2415) aNaturalNumber0(sz10) = all_18_1_20
% 223.00/172.19  																																																																																																																																																					| (1227) all_18_1_20 = 0
% 223.00/172.19  																																																																																																																																																					|
% 223.00/172.19  																																																																																																																																																						| From (1227) and (2415) follows:
% 223.00/172.19  																																																																																																																																																						| (61) aNaturalNumber0(sz10) = 0
% 223.00/172.19  																																																																																																																																																						|
% 223.00/172.19  																																																																																																																																																						+-Applying beta-rule and splitting (941), into two cases.
% 223.00/172.19  																																																																																																																																																						|-Branch one:
% 223.00/172.19  																																																																																																																																																						| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.00/172.19  																																																																																																																																																						|
% 223.00/172.19  																																																																																																																																																							| From (1283) and (2252) follows:
% 223.00/172.19  																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																							| Using (91) and (1934) yields:
% 223.00/172.19  																																																																																																																																																							| (1311) $false
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																							|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																						|-Branch two:
% 223.00/172.19  																																																																																																																																																						| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.00/172.19  																																																																																																																																																						| (2434) all_77_1_104 = all_26_2_33
% 223.00/172.19  																																																																																																																																																						|
% 223.00/172.19  																																																																																																																																																							| Combining equations (1246,2434) yields a new equation:
% 223.00/172.19  																																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																							| Combining equations (1283,2434) yields a new equation:
% 223.00/172.19  																																																																																																																																																							| (1246) all_77_1_104 = 0
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																							| From (1283) and (2255) follows:
% 223.00/172.19  																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																							+-Applying beta-rule and splitting (321), into two cases.
% 223.00/172.19  																																																																																																																																																							|-Branch one:
% 223.00/172.19  																																																																																																																																																							| (2426)  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																								| Using (1831) and (2426) yields:
% 223.00/172.19  																																																																																																																																																								| (1311) $false
% 223.00/172.19  																																																																																																																																																								|
% 223.00/172.19  																																																																																																																																																								|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																							|-Branch two:
% 223.00/172.19  																																																																																																																																																							| (1831) aNaturalNumber0(all_0_2_2) = 0
% 223.00/172.19  																																																																																																																																																							| (1829) all_67_2_97 = 0
% 223.00/172.19  																																																																																																																																																							|
% 223.00/172.19  																																																																																																																																																								+-Applying beta-rule and splitting (1083), into two cases.
% 223.00/172.19  																																																																																																																																																								|-Branch one:
% 223.00/172.19  																																																																																																																																																								| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.00/172.19  																																																																																																																																																								|
% 223.00/172.19  																																																																																																																																																									| From (1828) and (2446) follows:
% 223.00/172.19  																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.19  																																																																																																																																																									|
% 223.00/172.19  																																																																																																																																																									| Using (91) and (1934) yields:
% 223.00/172.19  																																																																																																																																																									| (1311) $false
% 223.00/172.19  																																																																																																																																																									|
% 223.00/172.19  																																																																																																																																																									|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																								|-Branch two:
% 223.00/172.19  																																																																																																																																																								| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.00/172.19  																																																																																																																																																								| (2450) all_20_0_22 = all_16_2_18
% 223.00/172.19  																																																																																																																																																								|
% 223.00/172.19  																																																																																																																																																									| From (1828) and (2449) follows:
% 223.00/172.19  																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.00/172.19  																																																																																																																																																									|
% 223.00/172.19  																																																																																																																																																									+-Applying beta-rule and splitting (592), into two cases.
% 223.00/172.19  																																																																																																																																																									|-Branch one:
% 223.00/172.19  																																																																																																																																																									| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.00/172.19  																																																																																																																																																									|
% 223.00/172.19  																																																																																																																																																										| From (1292) and (2023) follows:
% 223.00/172.19  																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																										| Using (9) and (2008) yields:
% 223.00/172.19  																																																																																																																																																										| (1311) $false
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																										|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																									|-Branch two:
% 223.00/172.19  																																																																																																																																																									| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.00/172.19  																																																																																																																																																									| (2442) all_57_3_91 = all_16_0_16
% 223.00/172.19  																																																																																																																																																									|
% 223.00/172.19  																																																																																																																																																										| Combining equations (2199,2442) yields a new equation:
% 223.00/172.19  																																																																																																																																																										| (1292) all_16_0_16 = 0
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																										| Combining equations (1292,2442) yields a new equation:
% 223.00/172.19  																																																																																																																																																										| (2199) all_57_3_91 = 0
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																										| From (1292) and (2026) follows:
% 223.00/172.19  																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																										+-Applying beta-rule and splitting (1076), into two cases.
% 223.00/172.19  																																																																																																																																																										|-Branch one:
% 223.00/172.19  																																																																																																																																																										| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																											| From (1221) and (2081) follows:
% 223.00/172.19  																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.19  																																																																																																																																																											|
% 223.00/172.19  																																																																																																																																																											| Using (91) and (1934) yields:
% 223.00/172.19  																																																																																																																																																											| (1311) $false
% 223.00/172.19  																																																																																																																																																											|
% 223.00/172.19  																																																																																																																																																											|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																										|-Branch two:
% 223.00/172.19  																																																																																																																																																										| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.00/172.19  																																																																																																																																																										| (2464) all_18_2_21 = all_12_1_11
% 223.00/172.19  																																																																																																																																																										|
% 223.00/172.19  																																																																																																																																																											| Combining equations (1226,2464) yields a new equation:
% 223.00/172.19  																																																																																																																																																											| (1221) all_12_1_11 = 0
% 223.00/172.19  																																																																																																																																																											|
% 223.00/172.19  																																																																																																																																																											| From (1221) and (2084) follows:
% 223.00/172.19  																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.00/172.19  																																																																																																																																																											|
% 223.00/172.19  																																																																																																																																																											+-Applying beta-rule and splitting (483), into two cases.
% 223.00/172.19  																																																																																																																																																											|-Branch one:
% 223.00/172.19  																																																																																																																																																											| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.00/172.19  																																																																																																																																																											|
% 223.00/172.19  																																																																																																																																																												| From (1281) and (1969) follows:
% 223.00/172.19  																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.00/172.19  																																																																																																																																																												|
% 223.00/172.19  																																																																																																																																																												| Using (12) and (1940) yields:
% 223.00/172.19  																																																																																																																																																												| (1311) $false
% 223.00/172.19  																																																																																																																																																												|
% 223.00/172.19  																																																																																																																																																												|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																											|-Branch two:
% 223.00/172.19  																																																																																																																																																											| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.00/172.19  																																																																																																																																																											| (1281) all_12_0_10 = 0
% 223.00/172.19  																																																																																																																																																											|
% 223.00/172.19  																																																																																																																																																												| From (1281) and (1972) follows:
% 223.00/172.19  																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.00/172.19  																																																																																																																																																												|
% 223.00/172.19  																																																																																																																																																												+-Applying beta-rule and splitting (643), into two cases.
% 223.00/172.19  																																																																																																																																																												|-Branch one:
% 223.00/172.19  																																																																																																																																																												| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.00/172.19  																																																																																																																																																												|
% 223.00/172.19  																																																																																																																																																													| From (1282) and (2475) follows:
% 223.00/172.19  																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.19  																																																																																																																																																													|
% 223.00/172.19  																																																																																																																																																													| Using (9) and (2008) yields:
% 223.00/172.19  																																																																																																																																																													| (1311) $false
% 223.00/172.19  																																																																																																																																																													|
% 223.00/172.19  																																																																																																																																																													|-The branch is then unsatisfiable
% 223.00/172.19  																																																																																																																																																												|-Branch two:
% 223.00/172.19  																																																																																																																																																												| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.00/172.19  																																																																																																																																																												| (2479) all_39_6_72 = all_24_2_30
% 223.00/172.19  																																																																																																																																																												|
% 223.00/172.19  																																																																																																																																																													| Combining equations (2479,629) yields a new equation:
% 223.00/172.20  																																																																																																																																																													| (5099) all_24_2_30 = 0
% 223.00/172.20  																																																																																																																																																													|
% 223.00/172.20  																																																																																																																																																													| Simplifying 5099 yields:
% 223.00/172.20  																																																																																																																																																													| (1282) all_24_2_30 = 0
% 223.00/172.20  																																																																																																																																																													|
% 223.00/172.20  																																																																																																																																																													| From (1282) and (2478) follows:
% 223.00/172.20  																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.00/172.20  																																																																																																																																																													|
% 223.00/172.20  																																																																																																																																																													+-Applying beta-rule and splitting (477), into two cases.
% 223.00/172.20  																																																																																																																																																													|-Branch one:
% 223.00/172.20  																																																																																																																																																													| (2467)  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 223.00/172.20  																																																																																																																																																													|
% 223.00/172.20  																																																																																																																																																														| From (1293) and (2467) follows:
% 223.00/172.20  																																																																																																																																																														| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																														| Using (1284) and (2090) yields:
% 223.00/172.20  																																																																																																																																																														| (1311) $false
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																														|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																													|-Branch two:
% 223.00/172.20  																																																																																																																																																													| (2470) aNaturalNumber0(all_0_9_9) = all_47_2_83
% 223.00/172.20  																																																																																																																																																													| (2471) all_47_2_83 = all_24_2_30
% 223.00/172.20  																																																																																																																																																													|
% 223.00/172.20  																																																																																																																																																														| Combining equations (1293,2471) yields a new equation:
% 223.00/172.20  																																																																																																																																																														| (1282) all_24_2_30 = 0
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																														| Combining equations (1282,2471) yields a new equation:
% 223.00/172.20  																																																																																																																																																														| (1293) all_47_2_83 = 0
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																														| From (1293) and (2470) follows:
% 223.00/172.20  																																																																																																																																																														| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																														+-Applying beta-rule and splitting (971), into two cases.
% 223.00/172.20  																																																																																																																																																														|-Branch one:
% 223.00/172.20  																																																																																																																																																														| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																															| From (1237) and (2490) follows:
% 223.00/172.20  																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																															| Using (91) and (1934) yields:
% 223.00/172.20  																																																																																																																																																															| (1311) $false
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																															|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																														|-Branch two:
% 223.00/172.20  																																																																																																																																																														| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.00/172.20  																																																																																																																																																														| (2494) all_62_1_93 = all_47_1_82
% 223.00/172.20  																																																																																																																																																														|
% 223.00/172.20  																																																																																																																																																															| Combining equations (1240,2494) yields a new equation:
% 223.00/172.20  																																																																																																																																																															| (1237) all_47_1_82 = 0
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																															| Combining equations (1237,2494) yields a new equation:
% 223.00/172.20  																																																																																																																																																															| (1240) all_62_1_93 = 0
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																															| From (1237) and (2493) follows:
% 223.00/172.20  																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																															+-Applying beta-rule and splitting (596), into two cases.
% 223.00/172.20  																																																																																																																																																															|-Branch one:
% 223.00/172.20  																																																																																																																																																															| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																																| From (1281) and (2039) follows:
% 223.00/172.20  																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.20  																																																																																																																																																																|
% 223.00/172.20  																																																																																																																																																																| Using (9) and (2008) yields:
% 223.00/172.20  																																																																																																																																																																| (1311) $false
% 223.00/172.20  																																																																																																																																																																|
% 223.00/172.20  																																																																																																																																																																|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																															|-Branch two:
% 223.00/172.20  																																																																																																																																																															| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.00/172.20  																																																																																																																																																															| (2487) all_57_3_91 = all_12_0_10
% 223.00/172.20  																																																																																																																																																															|
% 223.00/172.20  																																																																																																																																																																| Combining equations (2199,2487) yields a new equation:
% 223.00/172.20  																																																																																																																																																																| (1281) all_12_0_10 = 0
% 223.00/172.20  																																																																																																																																																																|
% 223.00/172.20  																																																																																																																																																																| From (1281) and (2042) follows:
% 223.00/172.20  																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.00/172.20  																																																																																																																																																																|
% 223.00/172.20  																																																																																																																																																																+-Applying beta-rule and splitting (554), into two cases.
% 223.00/172.20  																																																																																																																																																																|-Branch one:
% 223.00/172.20  																																																																																																																																																																| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.00/172.20  																																																																																																																																																																|
% 223.00/172.20  																																																																																																																																																																	| From (1790) and (2506) follows:
% 223.00/172.20  																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.00/172.20  																																																																																																																																																																	| (1311) $false
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																|-Branch two:
% 223.00/172.20  																																																																																																																																																																| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.00/172.20  																																																																																																																																																																| (2510) all_72_3_102 = all_62_2_94
% 223.00/172.20  																																																																																																																																																																|
% 223.00/172.20  																																																																																																																																																																	| Combining equations (1243,2510) yields a new equation:
% 223.00/172.20  																																																																																																																																																																	| (1790) all_62_2_94 = 0
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																	| Combining equations (1790,2510) yields a new equation:
% 223.00/172.20  																																																																																																																																																																	| (1243) all_72_3_102 = 0
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																	| From (1790) and (2509) follows:
% 223.00/172.20  																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																	+-Applying beta-rule and splitting (339), into two cases.
% 223.00/172.20  																																																																																																																																																																	|-Branch one:
% 223.00/172.20  																																																																																																																																																																	| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																		| From (1828) and (2498) follows:
% 223.00/172.20  																																																																																																																																																																		| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																		| Using (1775) and (1780) yields:
% 223.00/172.20  																																																																																																																																																																		| (1311) $false
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																	|-Branch two:
% 223.00/172.20  																																																																																																																																																																	| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 223.00/172.20  																																																																																																																																																																	| (2502) all_72_2_101 = all_20_0_22
% 223.00/172.20  																																																																																																																																																																	|
% 223.00/172.20  																																																																																																																																																																		| Combining equations (1791,2502) yields a new equation:
% 223.00/172.20  																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																		| Combining equations (1828,2502) yields a new equation:
% 223.00/172.20  																																																																																																																																																																		| (1791) all_72_2_101 = 0
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																		| From (1828) and (2501) follows:
% 223.00/172.20  																																																																																																																																																																		| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																		+-Applying beta-rule and splitting (1022), into two cases.
% 223.00/172.20  																																																																																																																																																																		|-Branch one:
% 223.00/172.20  																																																																																																																																																																		| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																			| From (1236) and (2522) follows:
% 223.00/172.20  																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.00/172.20  																																																																																																																																																																			| (1311) $false
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																		|-Branch two:
% 223.00/172.20  																																																																																																																																																																		| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.00/172.20  																																																																																																																																																																		| (2526) all_39_7_73 = all_39_8_74
% 223.00/172.20  																																																																																																																																																																		|
% 223.00/172.20  																																																																																																																																																																			| Combining equations (1236,2526) yields a new equation:
% 223.00/172.20  																																																																																																																																																																			| (1179) all_39_8_74 = 0
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																			| Combining equations (1179,2526) yields a new equation:
% 223.00/172.20  																																																																																																																																																																			| (1236) all_39_7_73 = 0
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																			| From (1236) and (2525) follows:
% 223.00/172.20  																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																			+-Applying beta-rule and splitting (531), into two cases.
% 223.00/172.20  																																																																																																																																																																			|-Branch one:
% 223.00/172.20  																																																																																																																																																																			| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																				| From (1283) and (2007) follows:
% 223.00/172.20  																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.00/172.20  																																																																																																																																																																				| (1311) $false
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																			|-Branch two:
% 223.00/172.20  																																																																																																																																																																			| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.00/172.20  																																																																																																																																																																			| (2518) all_82_3_110 = all_26_2_33
% 223.00/172.20  																																																																																																																																																																			|
% 223.00/172.20  																																																																																																																																																																				| Combining equations (1247,2518) yields a new equation:
% 223.00/172.20  																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																				| Combining equations (1283,2518) yields a new equation:
% 223.00/172.20  																																																																																																																																																																				| (1247) all_82_3_110 = 0
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																				| From (1283) and (2010) follows:
% 223.00/172.20  																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																				+-Applying beta-rule and splitting (1068), into two cases.
% 223.00/172.20  																																																																																																																																																																				|-Branch one:
% 223.00/172.20  																																																																																																																																																																				| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																					| From (1242) and (2334) follows:
% 223.00/172.20  																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.00/172.20  																																																																																																																																																																					| (1311) $false
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																				|-Branch two:
% 223.00/172.20  																																																																																																																																																																				| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.00/172.20  																																																																																																																																																																				| (2542) all_67_1_96 = all_18_2_21
% 223.00/172.20  																																																																																																																																																																				|
% 223.00/172.20  																																																																																																																																																																					| Combining equations (1242,2542) yields a new equation:
% 223.00/172.20  																																																																																																																																																																					| (1226) all_18_2_21 = 0
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																					| Combining equations (1226,2542) yields a new equation:
% 223.00/172.20  																																																																																																																																																																					| (1242) all_67_1_96 = 0
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																					| From (1242) and (2337) follows:
% 223.00/172.20  																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																					+-Applying beta-rule and splitting (546), into two cases.
% 223.00/172.20  																																																																																																																																																																					|-Branch one:
% 223.00/172.20  																																																																																																																																																																					| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																						| From (1283) and (2007) follows:
% 223.00/172.20  																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.00/172.20  																																																																																																																																																																						| (1311) $false
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																					|-Branch two:
% 223.00/172.20  																																																																																																																																																																					| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.00/172.20  																																																																																																																																																																					| (2534) all_77_3_106 = all_26_2_33
% 223.00/172.20  																																																																																																																																																																					|
% 223.00/172.20  																																																																																																																																																																						| Combining equations (1245,2534) yields a new equation:
% 223.00/172.20  																																																																																																																																																																						| (1283) all_26_2_33 = 0
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																						| Combining equations (1283,2534) yields a new equation:
% 223.00/172.20  																																																																																																																																																																						| (1245) all_77_3_106 = 0
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																						| From (1283) and (2010) follows:
% 223.00/172.20  																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																						+-Applying beta-rule and splitting (503), into two cases.
% 223.00/172.20  																																																																																																																																																																						|-Branch one:
% 223.00/172.20  																																																																																																																																																																						| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																							| From (1674) and (2552) follows:
% 223.00/172.20  																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.20  																																																																																																																																																																							|
% 223.00/172.20  																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.00/172.20  																																																																																																																																																																							| (1311) $false
% 223.00/172.20  																																																																																																																																																																							|
% 223.00/172.20  																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																						|-Branch two:
% 223.00/172.20  																																																																																																																																																																						| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.00/172.20  																																																																																																																																																																						| (1674) all_52_2_87 = 0
% 223.00/172.20  																																																																																																																																																																						|
% 223.00/172.20  																																																																																																																																																																							| From (1674) and (2555) follows:
% 223.00/172.20  																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.00/172.20  																																																																																																																																																																							|
% 223.00/172.20  																																																																																																																																																																							+-Applying beta-rule and splitting (851), into two cases.
% 223.00/172.20  																																																																																																																																																																							|-Branch one:
% 223.00/172.20  																																																																																																																																																																							| (2546)  ~ (aNaturalNumber0(sz00) = all_16_1_17)
% 223.00/172.20  																																																																																																																																																																							|
% 223.00/172.20  																																																																																																																																																																								| From (848) and (2546) follows:
% 223.00/172.20  																																																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.00/172.20  																																																																																																																																																																								|
% 223.00/172.20  																																																																																																																																																																								| Using (26) and (2070) yields:
% 223.00/172.20  																																																																																																																																																																								| (1311) $false
% 223.00/172.20  																																																																																																																																																																								|
% 223.00/172.20  																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																							|-Branch two:
% 223.00/172.20  																																																																																																																																																																							| (2549) aNaturalNumber0(sz00) = all_16_1_17
% 223.00/172.20  																																																																																																																																																																							| (848) all_16_1_17 = 0
% 223.00/172.20  																																																																																																																																																																							|
% 223.00/172.20  																																																																																																																																																																								| From (848) and (2549) follows:
% 223.00/172.20  																																																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 223.00/172.20  																																																																																																																																																																								|
% 223.00/172.20  																																																																																																																																																																								+-Applying beta-rule and splitting (855), into two cases.
% 223.00/172.20  																																																																																																																																																																								|-Branch one:
% 223.00/172.20  																																																																																																																																																																								| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.00/172.20  																																																																																																																																																																								|
% 223.00/172.20  																																																																																																																																																																									| From (1791) and (1977) follows:
% 223.00/172.20  																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.00/172.20  																																																																																																																																																																									| (1311) $false
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																								|-Branch two:
% 223.00/172.20  																																																																																																																																																																								| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.00/172.20  																																																																																																																																																																								| (2570) all_72_2_101 = all_16_1_17
% 223.00/172.20  																																																																																																																																																																								|
% 223.00/172.20  																																																																																																																																																																									| Combining equations (1791,2570) yields a new equation:
% 223.00/172.20  																																																																																																																																																																									| (848) all_16_1_17 = 0
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																									| Combining equations (848,2570) yields a new equation:
% 223.00/172.20  																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																									| From (1791) and (1980) follows:
% 223.00/172.20  																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																									+-Applying beta-rule and splitting (473), into two cases.
% 223.00/172.20  																																																																																																																																																																									|-Branch one:
% 223.00/172.20  																																																																																																																																																																									| (2558)  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																										| From (1789) and (2558) follows:
% 223.00/172.20  																																																																																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.00/172.20  																																																																																																																																																																										|
% 223.00/172.20  																																																																																																																																																																										| Using (1284) and (2090) yields:
% 223.00/172.20  																																																																																																																																																																										| (1311) $false
% 223.00/172.20  																																																																																																																																																																										|
% 223.00/172.20  																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.00/172.20  																																																																																																																																																																									|-Branch two:
% 223.00/172.20  																																																																																																																																																																									| (2561) aNaturalNumber0(all_0_9_9) = all_57_2_90
% 223.00/172.20  																																																																																																																																																																									| (2562) all_57_2_90 = all_24_2_30
% 223.00/172.20  																																																																																																																																																																									|
% 223.00/172.20  																																																																																																																																																																										| Combining equations (1789,2562) yields a new equation:
% 223.00/172.20  																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 223.00/172.20  																																																																																																																																																																										|
% 223.00/172.20  																																																																																																																																																																										| Combining equations (1282,2562) yields a new equation:
% 223.00/172.20  																																																																																																																																																																										| (1789) all_57_2_90 = 0
% 223.00/172.20  																																																																																																																																																																										|
% 223.00/172.20  																																																																																																																																																																										| From (1789) and (2561) follows:
% 223.00/172.20  																																																																																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.00/172.20  																																																																																																																																																																										|
% 223.00/172.20  																																																																																																																																																																										+-Applying beta-rule and splitting (929), into two cases.
% 223.00/172.20  																																																																																																																																																																										|-Branch one:
% 223.00/172.20  																																																																																																																																																																										| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.00/172.20  																																																																																																																																																																										|
% 223.00/172.20  																																																																																																																																																																											| From (848) and (2268) follows:
% 223.00/172.21  																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.00/172.21  																																																																																																																																																																											| (1311) $false
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.00/172.21  																																																																																																																																																																										|-Branch two:
% 223.00/172.21  																																																																																																																																																																										| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.00/172.21  																																																																																																																																																																										| (2586) all_82_1_108 = all_16_1_17
% 223.00/172.21  																																																																																																																																																																										|
% 223.00/172.21  																																																																																																																																																																											| Combining equations (1249,2586) yields a new equation:
% 223.00/172.21  																																																																																																																																																																											| (848) all_16_1_17 = 0
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																											| Combining equations (848,2586) yields a new equation:
% 223.00/172.21  																																																																																																																																																																											| (1249) all_82_1_108 = 0
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																											| From (848) and (2271) follows:
% 223.00/172.21  																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																											+-Applying beta-rule and splitting (437), into two cases.
% 223.00/172.21  																																																																																																																																																																											|-Branch one:
% 223.00/172.21  																																																																																																																																																																											| (2574)  ~ (aNaturalNumber0(all_0_8_8) = all_57_2_90)
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																												| From (1789) and (2574) follows:
% 223.00/172.21  																																																																																																																																																																												| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																												| Using (1351) and (2575) yields:
% 223.00/172.21  																																																																																																																																																																												| (1311) $false
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.00/172.21  																																																																																																																																																																											|-Branch two:
% 223.00/172.21  																																																																																																																																																																											| (2577) aNaturalNumber0(all_0_8_8) = all_57_2_90
% 223.00/172.21  																																																																																																																																																																											| (2578) all_57_2_90 = all_24_0_28
% 223.00/172.21  																																																																																																																																																																											|
% 223.00/172.21  																																																																																																																																																																												| Combining equations (1789,2578) yields a new equation:
% 223.00/172.21  																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																												| Combining equations (1350,2578) yields a new equation:
% 223.00/172.21  																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																												| From (1789) and (2577) follows:
% 223.00/172.21  																																																																																																																																																																												| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																												+-Applying beta-rule and splitting (924), into two cases.
% 223.00/172.21  																																																																																																																																																																												|-Branch one:
% 223.00/172.21  																																																																																																																																																																												| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																													| From (1236) and (2522) follows:
% 223.00/172.21  																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.00/172.21  																																																																																																																																																																													|
% 223.00/172.21  																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.00/172.21  																																																																																																																																																																													| (1311) $false
% 223.00/172.21  																																																																																																																																																																													|
% 223.00/172.21  																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.00/172.21  																																																																																																																																																																												|-Branch two:
% 223.00/172.21  																																																																																																																																																																												| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.00/172.21  																																																																																																																																																																												| (2600) all_82_1_108 = all_39_7_73
% 223.00/172.21  																																																																																																																																																																												|
% 223.00/172.21  																																																																																																																																																																													| Combining equations (1249,2600) yields a new equation:
% 223.00/172.21  																																																																																																																																																																													| (1236) all_39_7_73 = 0
% 223.00/172.21  																																																																																																																																																																													|
% 223.00/172.21  																																																																																																																																																																													| Combining equations (1236,2600) yields a new equation:
% 223.00/172.21  																																																																																																																																																																													| (1249) all_82_1_108 = 0
% 223.00/172.21  																																																																																																																																																																													|
% 223.00/172.21  																																																																																																																																																																													| From (1236) and (2525) follows:
% 223.00/172.21  																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.00/172.21  																																																																																																																																																																													|
% 223.00/172.21  																																																																																																																																																																													+-Applying beta-rule and splitting (359), into two cases.
% 223.00/172.21  																																																																																																																																																																													|-Branch one:
% 223.00/172.21  																																																																																																																																																																													| (2590)  ~ (aNaturalNumber0(xr) = all_22_2_27)
% 223.00/172.21  																																																																																																																																																																													|
% 223.00/172.21  																																																																																																																																																																														| From (1788) and (2590) follows:
% 223.00/172.21  																																																																																																																																																																														| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.00/172.21  																																																																																																																																																																														|
% 223.03/172.21  																																																																																																																																																																														| Using (88) and (8229) yields:
% 223.03/172.21  																																																																																																																																																																														| (1311) $false
% 223.03/172.21  																																																																																																																																																																														|
% 223.03/172.21  																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																													|-Branch two:
% 223.03/172.21  																																																																																																																																																																													| (2593) aNaturalNumber0(xr) = all_22_2_27
% 223.03/172.21  																																																																																																																																																																													| (1788) all_22_2_27 = 0
% 223.03/172.21  																																																																																																																																																																													|
% 223.03/172.21  																																																																																																																																																																														| From (1788) and (2593) follows:
% 223.03/172.21  																																																																																																																																																																														| (88) aNaturalNumber0(xr) = 0
% 223.03/172.21  																																																																																																																																																																														|
% 223.03/172.21  																																																																																																																																																																														+-Applying beta-rule and splitting (778), into two cases.
% 223.03/172.21  																																																																																																																																																																														|-Branch one:
% 223.03/172.21  																																																																																																																																																																														| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.03/172.21  																																																																																																																																																																														|
% 223.03/172.21  																																																																																																																																																																															| From (1789) and (1945) follows:
% 223.03/172.21  																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.03/172.21  																																																																																																																																																																															| (1311) $false
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																														|-Branch two:
% 223.03/172.21  																																																																																																																																																																														| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.03/172.21  																																																																																																																																																																														| (2616) all_57_2_90 = all_37_3_64
% 223.03/172.21  																																																																																																																																																																														|
% 223.03/172.21  																																																																																																																																																																															| Combining equations (1789,2616) yields a new equation:
% 223.03/172.21  																																																																																																																																																																															| (1233) all_37_3_64 = 0
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																															| Combining equations (1233,2616) yields a new equation:
% 223.03/172.21  																																																																																																																																																																															| (1789) all_57_2_90 = 0
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																															| From (1789) and (1948) follows:
% 223.03/172.21  																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																															+-Applying beta-rule and splitting (1142), into two cases.
% 223.03/172.21  																																																																																																																																																																															|-Branch one:
% 223.03/172.21  																																																																																																																																																																															| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																																| From (1244) and (2604) follows:
% 223.03/172.21  																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.03/172.21  																																																																																																																																																																																| (1311) $false
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																															|-Branch two:
% 223.03/172.21  																																																																																																																																																																															| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.03/172.21  																																																																																																																																																																															| (2608) all_72_1_100 = all_12_2_12
% 223.03/172.21  																																																																																																																																																																															|
% 223.03/172.21  																																																																																																																																																																																| Combining equations (1244,2608) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																| (1223) all_12_2_12 = 0
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																| Combining equations (1223,2608) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																| (1244) all_72_1_100 = 0
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																| From (1244) and (2607) follows:
% 223.03/172.21  																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																+-Applying beta-rule and splitting (836), into two cases.
% 223.03/172.21  																																																																																																																																																																																|-Branch one:
% 223.03/172.21  																																																																																																																																																																																| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																	| From (1789) and (1945) follows:
% 223.03/172.21  																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.03/172.21  																																																																																																																																																																																	| (1311) $false
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																																|-Branch two:
% 223.03/172.21  																																																																																																																																																																																| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.03/172.21  																																																																																																																																																																																| (2632) all_57_2_90 = all_18_1_20
% 223.03/172.21  																																																																																																																																																																																|
% 223.03/172.21  																																																																																																																																																																																	| Combining equations (1789,2632) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																	| (1227) all_18_1_20 = 0
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																	| Combining equations (1227,2632) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																	| (1789) all_57_2_90 = 0
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																	| From (1789) and (1948) follows:
% 223.03/172.21  																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																	+-Applying beta-rule and splitting (407), into two cases.
% 223.03/172.21  																																																																																																																																																																																	|-Branch one:
% 223.03/172.21  																																																																																																																																																																																	| (2620)  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																		| From (1788) and (2620) follows:
% 223.03/172.21  																																																																																																																																																																																		| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																		| Using (1295) and (2129) yields:
% 223.03/172.21  																																																																																																																																																																																		| (1311) $false
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																																	|-Branch two:
% 223.03/172.21  																																																																																																																																																																																	| (2623) aNaturalNumber0(all_0_7_7) = all_22_2_27
% 223.03/172.21  																																																																																																																																																																																	| (2624) all_47_2_83 = all_22_2_27
% 223.03/172.21  																																																																																																																																																																																	|
% 223.03/172.21  																																																																																																																																																																																		| Combining equations (1293,2624) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																		| (1788) all_22_2_27 = 0
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																		| Combining equations (1788,2624) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																		| From (1788) and (2623) follows:
% 223.03/172.21  																																																																																																																																																																																		| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																		+-Applying beta-rule and splitting (682), into two cases.
% 223.03/172.21  																																																																																																																																																																																		|-Branch one:
% 223.03/172.21  																																																																																																																																																																																		| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																			| From (1791) and (2642) follows:
% 223.03/172.21  																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.03/172.21  																																																																																																																																																																																			| (1311) $false
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																																		|-Branch two:
% 223.03/172.21  																																																																																																																																																																																		| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.03/172.21  																																																																																																																																																																																		| (2646) all_72_2_101 = all_24_1_29
% 223.03/172.21  																																																																																																																																																																																		|
% 223.03/172.21  																																																																																																																																																																																			| Combining equations (1791,2646) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																			| (1207) all_24_1_29 = 0
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																			| Combining equations (1207,2646) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																			| (1791) all_72_2_101 = 0
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																			| From (1791) and (2645) follows:
% 223.03/172.21  																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																			+-Applying beta-rule and splitting (696), into two cases.
% 223.03/172.21  																																																																																																																																																																																			|-Branch one:
% 223.03/172.21  																																																																																																																																																																																			| (2636)  ~ (aNaturalNumber0(sz10) = all_72_1_100)
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																				| From (1244) and (2636) follows:
% 223.03/172.21  																																																																																																																																																																																				| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.03/172.21  																																																																																																																																																																																				|
% 223.03/172.21  																																																																																																																																																																																				| Using (61) and (1994) yields:
% 223.03/172.21  																																																																																																																																																																																				| (1311) $false
% 223.03/172.21  																																																																																																																																																																																				|
% 223.03/172.21  																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																																			|-Branch two:
% 223.03/172.21  																																																																																																																																																																																			| (2639) aNaturalNumber0(sz10) = all_72_1_100
% 223.03/172.21  																																																																																																																																																																																			| (1244) all_72_1_100 = 0
% 223.03/172.21  																																																																																																																																																																																			|
% 223.03/172.21  																																																																																																																																																																																				| From (1244) and (2639) follows:
% 223.03/172.21  																																																																																																																																																																																				| (61) aNaturalNumber0(sz10) = 0
% 223.03/172.21  																																																																																																																																																																																				|
% 223.03/172.21  																																																																																																																																																																																				+-Applying beta-rule and splitting (570), into two cases.
% 223.03/172.21  																																																																																																																																																																																				|-Branch one:
% 223.03/172.21  																																																																																																																																																																																				| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.03/172.21  																																																																																																																																																																																				|
% 223.03/172.21  																																																																																																																																																																																					| From (1790) and (2506) follows:
% 223.03/172.21  																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.21  																																																																																																																																																																																					|
% 223.03/172.21  																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.03/172.21  																																																																																																																																																																																					| (1311) $false
% 223.03/172.21  																																																																																																																																																																																					|
% 223.03/172.21  																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																																				|-Branch two:
% 223.03/172.21  																																																																																																																																																																																				| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.03/172.21  																																																																																																																																																																																				| (2662) all_67_3_98 = all_62_2_94
% 223.03/172.21  																																																																																																																																																																																				|
% 223.03/172.21  																																																																																																																																																																																					| Combining equations (1241,2662) yields a new equation:
% 223.03/172.21  																																																																																																																																																																																					| (1790) all_62_2_94 = 0
% 223.03/172.21  																																																																																																																																																																																					|
% 223.03/172.21  																																																																																																																																																																																					| From (1790) and (2509) follows:
% 223.03/172.21  																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.03/172.21  																																																																																																																																																																																					|
% 223.03/172.21  																																																																																																																																																																																					+-Applying beta-rule and splitting (648), into two cases.
% 223.03/172.21  																																																																																																																																																																																					|-Branch one:
% 223.03/172.21  																																																																																																																																																																																					| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.03/172.21  																																																																																																																																																																																					|
% 223.03/172.21  																																																																																																																																																																																						| From (1791) and (2642) follows:
% 223.03/172.21  																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.21  																																																																																																																																																																																						|
% 223.03/172.21  																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.03/172.21  																																																																																																																																																																																						| (1311) $false
% 223.03/172.21  																																																																																																																																																																																						|
% 223.03/172.21  																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.03/172.21  																																																																																																																																																																																					|-Branch two:
% 223.03/172.21  																																																																																																																																																																																					| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.03/172.22  																																																																																																																																																																																					| (2654) all_72_2_101 = all_37_2_63
% 223.03/172.22  																																																																																																																																																																																					|
% 223.03/172.22  																																																																																																																																																																																						| Combining equations (1791,2654) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																						| (1195) all_37_2_63 = 0
% 223.03/172.22  																																																																																																																																																																																						|
% 223.03/172.22  																																																																																																																																																																																						| Combining equations (1195,2654) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																						| (1791) all_72_2_101 = 0
% 223.03/172.22  																																																																																																																																																																																						|
% 223.03/172.22  																																																																																																																																																																																						| From (1791) and (2645) follows:
% 223.03/172.22  																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.03/172.22  																																																																																																																																																																																						|
% 223.03/172.22  																																																																																																																																																																																						+-Applying beta-rule and splitting (567), into two cases.
% 223.03/172.22  																																																																																																																																																																																						|-Branch one:
% 223.03/172.22  																																																																																																																																																																																						| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.03/172.22  																																																																																																																																																																																						|
% 223.03/172.22  																																																																																																																																																																																							| From (1829) and (2665) follows:
% 223.03/172.22  																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.03/172.22  																																																																																																																																																																																							| (1311) $false
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																						|-Branch two:
% 223.03/172.22  																																																																																																																																																																																						| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.03/172.22  																																																																																																																																																																																						| (2677) all_67_2_97 = all_67_3_98
% 223.03/172.22  																																																																																																																																																																																						|
% 223.03/172.22  																																																																																																																																																																																							| Combining equations (1829,2677) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																							| (1241) all_67_3_98 = 0
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																							| Combining equations (1241,2677) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																							| From (1829) and (2668) follows:
% 223.03/172.22  																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																							+-Applying beta-rule and splitting (583), into two cases.
% 223.03/172.22  																																																																																																																																																																																							|-Branch one:
% 223.03/172.22  																																																																																																																																																																																							| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																								| From (1829) and (2665) follows:
% 223.03/172.22  																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.03/172.22  																																																																																																																																																																																								| (1311) $false
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																							|-Branch two:
% 223.03/172.22  																																																																																																																																																																																							| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.03/172.22  																																																																																																																																																																																							| (2669) all_67_2_97 = all_57_3_91
% 223.03/172.22  																																																																																																																																																																																							|
% 223.03/172.22  																																																																																																																																																																																								| Combining equations (1829,2669) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																								| (2199) all_57_3_91 = 0
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																								| Combining equations (2199,2669) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																								| From (1829) and (2668) follows:
% 223.03/172.22  																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																								+-Applying beta-rule and splitting (617), into two cases.
% 223.03/172.22  																																																																																																																																																																																								|-Branch one:
% 223.03/172.22  																																																																																																																																																																																								| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																									| From (1790) and (2506) follows:
% 223.03/172.22  																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.03/172.22  																																																																																																																																																																																									| (1311) $false
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																								|-Branch two:
% 223.03/172.22  																																																																																																																																																																																								| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.03/172.22  																																																																																																																																																																																								| (2693) all_62_2_94 = all_47_3_84
% 223.03/172.22  																																																																																																																																																																																								|
% 223.03/172.22  																																																																																																																																																																																									| Combining equations (1790,2693) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																									| (2191) all_47_3_84 = 0
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																									| Combining equations (2191,2693) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																									| (1790) all_62_2_94 = 0
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																									| From (1790) and (2509) follows:
% 223.03/172.22  																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																									+-Applying beta-rule and splitting (1064), into two cases.
% 223.03/172.22  																																																																																																																																																																																									|-Branch one:
% 223.03/172.22  																																																																																																																																																																																									| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																										| From (1282) and (2210) follows:
% 223.03/172.22  																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.03/172.22  																																																																																																																																																																																										| (1311) $false
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																									|-Branch two:
% 223.03/172.22  																																																																																																																																																																																									| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.03/172.22  																																																																																																																																																																																									| (2685) all_24_2_30 = all_18_2_21
% 223.03/172.22  																																																																																																																																																																																									|
% 223.03/172.22  																																																																																																																																																																																										| Combining equations (1282,2685) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																										| (1226) all_18_2_21 = 0
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																										| Combining equations (1226,2685) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																										| From (1282) and (2213) follows:
% 223.03/172.22  																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																										+-Applying beta-rule and splitting (837), into two cases.
% 223.03/172.22  																																																																																																																																																																																										|-Branch one:
% 223.03/172.22  																																																																																																																																																																																										| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																											| From (1788) and (2144) follows:
% 223.03/172.22  																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.03/172.22  																																																																																																																																																																																											|
% 223.03/172.22  																																																																																																																																																																																											| Using (12) and (1940) yields:
% 223.03/172.22  																																																																																																																																																																																											| (1311) $false
% 223.03/172.22  																																																																																																																																																																																											|
% 223.03/172.22  																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																										|-Branch two:
% 223.03/172.22  																																																																																																																																																																																										| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.03/172.22  																																																																																																																																																																																										| (2709) all_22_2_27 = all_18_1_20
% 223.03/172.22  																																																																																																																																																																																										|
% 223.03/172.22  																																																																																																																																																																																											| From (1788) and (2147) follows:
% 223.03/172.22  																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 223.03/172.22  																																																																																																																																																																																											|
% 223.03/172.22  																																																																																																																																																																																											+-Applying beta-rule and splitting (588), into two cases.
% 223.03/172.22  																																																																																																																																																																																											|-Branch one:
% 223.03/172.22  																																																																																																																																																																																											| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.03/172.22  																																																																																																																																																																																											|
% 223.03/172.22  																																																																																																																																																																																												| From (1788) and (2105) follows:
% 223.03/172.22  																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.03/172.22  																																																																																																																																																																																												| (1311) $false
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																											|-Branch two:
% 223.03/172.22  																																																																																																																																																																																											| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.03/172.22  																																																																																																																																																																																											| (2701) all_57_3_91 = all_22_2_27
% 223.03/172.22  																																																																																																																																																																																											|
% 223.03/172.22  																																																																																																																																																																																												| Combining equations (2199,2701) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																												| Combining equations (1788,2701) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																												| (2199) all_57_3_91 = 0
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																												| From (1788) and (2108) follows:
% 223.03/172.22  																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																												+-Applying beta-rule and splitting (348), into two cases.
% 223.03/172.22  																																																																																																																																																																																												|-Branch one:
% 223.03/172.22  																																																																																																																																																																																												| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																													| From (1828) and (2498) follows:
% 223.03/172.22  																																																																																																																																																																																													| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																													| Using (1775) and (1780) yields:
% 223.03/172.22  																																																																																																																																																																																													| (1311) $false
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																												|-Branch two:
% 223.03/172.22  																																																																																																																																																																																												| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 223.03/172.22  																																																																																																																																																																																												| (2723) all_62_2_94 = all_20_0_22
% 223.03/172.22  																																																																																																																																																																																												|
% 223.03/172.22  																																																																																																																																																																																													| Combining equations (1790,2723) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																													| (1828) all_20_0_22 = 0
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																													| Combining equations (1828,2723) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																													| (1790) all_62_2_94 = 0
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																													| From (1828) and (2501) follows:
% 223.03/172.22  																																																																																																																																																																																													| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																													+-Applying beta-rule and splitting (839), into two cases.
% 223.03/172.22  																																																																																																																																																																																													|-Branch one:
% 223.03/172.22  																																																																																																																																																																																													| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																														| From (1294) and (2275) follows:
% 223.03/172.22  																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.03/172.22  																																																																																																																																																																																														| (1311) $false
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																													|-Branch two:
% 223.03/172.22  																																																																																																																																																																																													| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.03/172.22  																																																																																																																																																																																													| (2715) all_77_2_105 = all_18_1_20
% 223.03/172.22  																																																																																																																																																																																													|
% 223.03/172.22  																																																																																																																																																																																														| Combining equations (1294,2715) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																														| (1227) all_18_1_20 = 0
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																														| Combining equations (1227,2715) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																														| From (1294) and (2278) follows:
% 223.03/172.22  																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																														+-Applying beta-rule and splitting (431), into two cases.
% 223.03/172.22  																																																																																																																																																																																														|-Branch one:
% 223.03/172.22  																																																																																																																																																																																														| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																															| Using (1351) and (2575) yields:
% 223.03/172.22  																																																																																																																																																																																															| (1311) $false
% 223.03/172.22  																																																																																																																																																																																															|
% 223.03/172.22  																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																														|-Branch two:
% 223.03/172.22  																																																																																																																																																																																														| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.03/172.22  																																																																																																																																																																																														| (1350) all_24_0_28 = 0
% 223.03/172.22  																																																																																																																																																																																														|
% 223.03/172.22  																																																																																																																																																																																															+-Applying beta-rule and splitting (979), into two cases.
% 223.03/172.22  																																																																																																																																																																																															|-Branch one:
% 223.03/172.22  																																																																																																																																																																																															| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.03/172.22  																																																																																																																																																																																															|
% 223.03/172.22  																																																																																																																																																																																																| From (1221) and (2081) follows:
% 223.03/172.22  																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.03/172.22  																																																																																																																																																																																																| (1311) $false
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																															|-Branch two:
% 223.03/172.22  																																																																																																																																																																																															| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.03/172.22  																																																																																																																																																																																															| (2731) all_62_1_93 = all_12_1_11
% 223.03/172.22  																																																																																																																																																																																															|
% 223.03/172.22  																																																																																																																																																																																																| Combining equations (1240,2731) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																																| (1221) all_12_1_11 = 0
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																| Combining equations (1221,2731) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																																| (1240) all_62_1_93 = 0
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																| From (1221) and (2084) follows:
% 223.03/172.22  																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																+-Applying beta-rule and splitting (943), into two cases.
% 223.03/172.22  																																																																																																																																																																																																|-Branch one:
% 223.03/172.22  																																																																																																																																																																																																| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																	| From (1281) and (2374) follows:
% 223.03/172.22  																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.03/172.22  																																																																																																																																																																																																	| (1311) $false
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																																|-Branch two:
% 223.03/172.22  																																																																																																																																																																																																| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.03/172.22  																																																																																																																																																																																																| (2751) all_77_1_104 = all_12_0_10
% 223.03/172.22  																																																																																																																																																																																																|
% 223.03/172.22  																																																																																																																																																																																																	| Combining equations (1246,2751) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																	| Combining equations (1281,2751) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																																	| (1246) all_77_1_104 = 0
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																	| From (1281) and (2377) follows:
% 223.03/172.22  																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																	+-Applying beta-rule and splitting (1038), into two cases.
% 223.03/172.22  																																																																																																																																																																																																	|-Branch one:
% 223.03/172.22  																																																																																																																																																																																																	| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																		| From (1350) and (1985) follows:
% 223.03/172.22  																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.03/172.22  																																																																																																																																																																																																		| (1311) $false
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																																	|-Branch two:
% 223.03/172.22  																																																																																																																																																																																																	| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.03/172.22  																																																																																																																																																																																																	| (2743) all_37_4_65 = all_24_0_28
% 223.03/172.22  																																																																																																																																																																																																	|
% 223.03/172.22  																																																																																																																																																																																																		| Combining equations (1232,2743) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																																		| (1350) all_24_0_28 = 0
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																		| Combining equations (1350,2743) yields a new equation:
% 223.03/172.22  																																																																																																																																																																																																		| (1232) all_37_4_65 = 0
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																		| From (1350) and (1988) follows:
% 223.03/172.22  																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																		+-Applying beta-rule and splitting (341), into two cases.
% 223.03/172.22  																																																																																																																																																																																																		|-Branch one:
% 223.03/172.22  																																																																																																																																																																																																		| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																			| From (1790) and (2506) follows:
% 223.03/172.22  																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.22  																																																																																																																																																																																																			|
% 223.03/172.22  																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.03/172.22  																																																																																																																																																																																																			| (1311) $false
% 223.03/172.22  																																																																																																																																																																																																			|
% 223.03/172.22  																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.03/172.22  																																																																																																																																																																																																		|-Branch two:
% 223.03/172.22  																																																																																																																																																																																																		| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.03/172.22  																																																																																																																																																																																																		| (1790) all_62_2_94 = 0
% 223.03/172.22  																																																																																																																																																																																																		|
% 223.03/172.22  																																																																																																																																																																																																			| From (1790) and (2509) follows:
% 223.03/172.23  																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.03/172.23  																																																																																																																																																																																																			|
% 223.03/172.23  																																																																																																																																																																																																			+-Applying beta-rule and splitting (420), into two cases.
% 223.03/172.23  																																																																																																																																																																																																			|-Branch one:
% 223.03/172.23  																																																																																																																																																																																																			| (2755)  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 223.03/172.23  																																																																																																																																																																																																			|
% 223.03/172.23  																																																																																																																																																																																																				| From (1790) and (2755) follows:
% 223.03/172.23  																																																																																																																																																																																																				| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																				| Using (1295) and (2129) yields:
% 223.03/172.23  																																																																																																																																																																																																				| (1311) $false
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.03/172.23  																																																																																																																																																																																																			|-Branch two:
% 223.03/172.23  																																																																																																																																																																																																			| (2758) aNaturalNumber0(all_0_7_7) = all_62_2_94
% 223.03/172.23  																																																																																																																																																																																																			| (2759) all_62_2_94 = all_16_0_16
% 223.03/172.23  																																																																																																																																																																																																			|
% 223.03/172.23  																																																																																																																																																																																																				| Combining equations (1790,2759) yields a new equation:
% 223.03/172.23  																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																				| Combining equations (1292,2759) yields a new equation:
% 223.03/172.23  																																																																																																																																																																																																				| (1790) all_62_2_94 = 0
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																				| From (1790) and (2758) follows:
% 223.03/172.23  																																																																																																																																																																																																				| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																				+-Applying beta-rule and splitting (923), into two cases.
% 223.03/172.23  																																																																																																																																																																																																				|-Branch one:
% 223.03/172.23  																																																																																																																																																																																																				| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																					| From (1237) and (2490) follows:
% 223.03/172.23  																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.03/172.23  																																																																																																																																																																																																					| (1311) $false
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.03/172.23  																																																																																																																																																																																																				|-Branch two:
% 223.03/172.23  																																																																																																																																																																																																				| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.03/172.23  																																																																																																																																																																																																				| (2781) all_82_1_108 = all_47_1_82
% 223.03/172.23  																																																																																																																																																																																																				|
% 223.03/172.23  																																																																																																																																																																																																					| Combining equations (1249,2781) yields a new equation:
% 223.03/172.23  																																																																																																																																																																																																					| (1237) all_47_1_82 = 0
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																					| Combining equations (1237,2781) yields a new equation:
% 223.03/172.23  																																																																																																																																																																																																					| (1249) all_82_1_108 = 0
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																					| From (1237) and (2493) follows:
% 223.03/172.23  																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																					+-Applying beta-rule and splitting (669), into two cases.
% 223.03/172.23  																																																																																																																																																																																																					|-Branch one:
% 223.03/172.23  																																																																																																																																																																																																					| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																						| From (1788) and (2105) follows:
% 223.03/172.23  																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.03/172.23  																																																																																																																																																																																																						|
% 223.03/172.23  																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.03/172.23  																																																																																																																																																																																																						| (1311) $false
% 223.03/172.23  																																																																																																																																																																																																						|
% 223.03/172.23  																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.03/172.23  																																																																																																																																																																																																					|-Branch two:
% 223.03/172.23  																																																																																																																																																																																																					| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.03/172.23  																																																																																																																																																																																																					| (2773) all_26_1_32 = all_22_2_27
% 223.03/172.23  																																																																																																																																																																																																					|
% 223.03/172.23  																																																																																																																																																																																																						| Combining equations (1202,2773) yields a new equation:
% 223.03/172.23  																																																																																																																																																																																																						| (1788) all_22_2_27 = 0
% 223.03/172.23  																																																																																																																																																																																																						|
% 223.03/172.23  																																																																																																																																																																																																						| Combining equations (1788,2773) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																						| (1202) all_26_1_32 = 0
% 223.07/172.23  																																																																																																																																																																																																						|
% 223.07/172.23  																																																																																																																																																																																																						| From (1788) and (2108) follows:
% 223.07/172.23  																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.07/172.23  																																																																																																																																																																																																						|
% 223.07/172.23  																																																																																																																																																																																																						+-Applying beta-rule and splitting (602), into two cases.
% 223.07/172.23  																																																																																																																																																																																																						|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																						| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.07/172.23  																																																																																																																																																																																																						|
% 223.07/172.23  																																																																																																																																																																																																							| From (1789) and (2186) follows:
% 223.07/172.23  																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.07/172.23  																																																																																																																																																																																																							| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																						|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																						| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.07/172.23  																																																																																																																																																																																																						| (2797) all_57_2_90 = all_52_1_86
% 223.07/172.23  																																																																																																																																																																																																						|
% 223.07/172.23  																																																																																																																																																																																																							| Combining equations (1789,2797) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																							| (1238) all_52_1_86 = 0
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																							| Combining equations (1238,2797) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																							| (1789) all_57_2_90 = 0
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																							| From (1789) and (2189) follows:
% 223.07/172.23  																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																							+-Applying beta-rule and splitting (720), into two cases.
% 223.07/172.23  																																																																																																																																																																																																							|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																							| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																								| From (1790) and (1939) follows:
% 223.07/172.23  																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.07/172.23  																																																																																																																																																																																																								| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																							|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																							| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.07/172.23  																																																																																																																																																																																																							| (2789) all_67_1_96 = all_62_2_94
% 223.07/172.23  																																																																																																																																																																																																							|
% 223.07/172.23  																																																																																																																																																																																																								| Combining equations (1242,2789) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																								| (1790) all_62_2_94 = 0
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																								| Combining equations (1790,2789) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																								| (1242) all_67_1_96 = 0
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																								| From (1790) and (1942) follows:
% 223.07/172.23  																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																								+-Applying beta-rule and splitting (441), into two cases.
% 223.07/172.23  																																																																																																																																																																																																								|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																								| (2809)  ~ (aNaturalNumber0(all_0_8_8) = all_47_2_83)
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																									| From (1293) and (2809) follows:
% 223.07/172.23  																																																																																																																																																																																																									| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																									| Using (1351) and (2575) yields:
% 223.07/172.23  																																																																																																																																																																																																									| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																								|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																								| (2812) aNaturalNumber0(all_0_8_8) = all_47_2_83
% 223.07/172.23  																																																																																																																																																																																																								| (2813) all_47_2_83 = all_24_0_28
% 223.07/172.23  																																																																																																																																																																																																								|
% 223.07/172.23  																																																																																																																																																																																																									| Combining equations (1293,2813) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																									| (1350) all_24_0_28 = 0
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																									| Combining equations (1350,2813) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																									| (1293) all_47_2_83 = 0
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																									| From (1293) and (2812) follows:
% 223.07/172.23  																																																																																																																																																																																																									| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																									+-Applying beta-rule and splitting (504), into two cases.
% 223.07/172.23  																																																																																																																																																																																																									|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																									| (2801)  ~ (aNaturalNumber0(xk) = all_82_2_109)
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																										| From (1830) and (2801) follows:
% 223.07/172.23  																																																																																																																																																																																																										| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																										| Using (1665) and (1670) yields:
% 223.07/172.23  																																																																																																																																																																																																										| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																									|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																									| (2804) aNaturalNumber0(xk) = all_82_2_109
% 223.07/172.23  																																																																																																																																																																																																									| (2805) all_82_2_109 = all_52_2_87
% 223.07/172.23  																																																																																																																																																																																																									|
% 223.07/172.23  																																																																																																																																																																																																										| Combining equations (1830,2805) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																										| (1674) all_52_2_87 = 0
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																										| Combining equations (1674,2805) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																										| From (1830) and (2804) follows:
% 223.07/172.23  																																																																																																																																																																																																										| (1665) aNaturalNumber0(xk) = 0
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																										+-Applying beta-rule and splitting (800), into two cases.
% 223.07/172.23  																																																																																																																																																																																																										|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																										| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																											| From (1789) and (1945) follows:
% 223.07/172.23  																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 223.07/172.23  																																																																																																																																																																																																											| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																										|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																										| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.07/172.23  																																																																																																																																																																																																										| (2829) all_57_2_90 = all_22_1_26
% 223.07/172.23  																																																																																																																																																																																																										|
% 223.07/172.23  																																																																																																																																																																																																											| Combining equations (1789,2829) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																											| (1229) all_22_1_26 = 0
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																											| Combining equations (1229,2829) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																											| (1789) all_57_2_90 = 0
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																											| From (1789) and (1948) follows:
% 223.07/172.23  																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																											+-Applying beta-rule and splitting (765), into two cases.
% 223.07/172.23  																																																																																																																																																																																																											|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																											| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																												| From (1350) and (2136) follows:
% 223.07/172.23  																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.07/172.23  																																																																																																																																																																																																												| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																											|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																											| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.07/172.23  																																																																																																																																																																																																											| (2821) all_39_7_73 = all_24_0_28
% 223.07/172.23  																																																																																																																																																																																																											|
% 223.07/172.23  																																																																																																																																																																																																												| Combining equations (1236,2821) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																												| Combining equations (1350,2821) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																												| (1236) all_39_7_73 = 0
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																												| From (1350) and (2139) follows:
% 223.07/172.23  																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																												+-Applying beta-rule and splitting (950), into two cases.
% 223.07/172.23  																																																																																																																																																																																																												|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																												| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																													| From (1228) and (2055) follows:
% 223.07/172.23  																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.07/172.23  																																																																																																																																																																																																													| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																												|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																												| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.07/172.23  																																																																																																																																																																																																												| (2845) all_77_1_104 = all_20_1_23
% 223.07/172.23  																																																																																																																																																																																																												|
% 223.07/172.23  																																																																																																																																																																																																													| Combining equations (1246,2845) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																													| (1228) all_20_1_23 = 0
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																													| Combining equations (1228,2845) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																													| (1246) all_77_1_104 = 0
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																													| From (1228) and (2058) follows:
% 223.07/172.23  																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																													+-Applying beta-rule and splitting (651), into two cases.
% 223.07/172.23  																																																																																																																																																																																																													|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																													| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																														| From (1788) and (2105) follows:
% 223.07/172.23  																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 223.07/172.23  																																																																																																																																																																																																														| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																													|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																													| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.07/172.23  																																																																																																																																																																																																													| (2837) all_37_2_63 = all_22_2_27
% 223.07/172.23  																																																																																																																																																																																																													|
% 223.07/172.23  																																																																																																																																																																																																														| Combining equations (1195,2837) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																														| (1788) all_22_2_27 = 0
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																														| Combining equations (1788,2837) yields a new equation:
% 223.07/172.23  																																																																																																																																																																																																														| (1195) all_37_2_63 = 0
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																														| From (1788) and (2108) follows:
% 223.07/172.23  																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																														+-Applying beta-rule and splitting (362), into two cases.
% 223.07/172.23  																																																																																																																																																																																																														|-Branch one:
% 223.07/172.23  																																																																																																																																																																																																														| (2855)  ~ (aNaturalNumber0(sz10) = all_22_2_27)
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																															| From (1788) and (2855) follows:
% 223.07/172.23  																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.07/172.23  																																																																																																																																																																																																															|
% 223.07/172.23  																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 223.07/172.23  																																																																																																																																																																																																															| (1311) $false
% 223.07/172.23  																																																																																																																																																																																																															|
% 223.07/172.23  																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.23  																																																																																																																																																																																																														|-Branch two:
% 223.07/172.23  																																																																																																																																																																																																														| (2858) aNaturalNumber0(sz10) = all_22_2_27
% 223.07/172.23  																																																																																																																																																																																																														| (1788) all_22_2_27 = 0
% 223.07/172.23  																																																																																																																																																																																																														|
% 223.07/172.23  																																																																																																																																																																																																															| From (1788) and (2858) follows:
% 223.07/172.23  																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 223.07/172.23  																																																																																																																																																																																																															|
% 223.07/172.23  																																																																																																																																																																																																															+-Applying beta-rule and splitting (1100), into two cases.
% 223.07/172.23  																																																																																																																																																																																																															|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																															| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.07/172.24  																																																																																																																																																																																																															|
% 223.07/172.24  																																																																																																																																																																																																																| From (848) and (2268) follows:
% 223.07/172.24  																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.07/172.24  																																																																																																																																																																																																																| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																															|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																															| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.07/172.24  																																																																																																																																																																																																															| (2853) all_16_1_17 = all_16_2_18
% 223.07/172.24  																																																																																																																																																																																																															|
% 223.07/172.24  																																																																																																																																																																																																																| Combining equations (848,2853) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																| (1225) all_16_2_18 = 0
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																| Combining equations (1225,2853) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																| (848) all_16_1_17 = 0
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																| From (848) and (2271) follows:
% 223.07/172.24  																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																+-Applying beta-rule and splitting (1087), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																	| From (1350) and (1985) follows:
% 223.07/172.24  																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.24  																																																																																																																																																																																																																	|
% 223.07/172.24  																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.07/172.24  																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																	|
% 223.07/172.24  																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.07/172.24  																																																																																																																																																																																																																| (2872) all_24_0_28 = all_16_2_18
% 223.07/172.24  																																																																																																																																																																																																																|
% 223.07/172.24  																																																																																																																																																																																																																	| From (1350) and (1988) follows:
% 223.07/172.24  																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.07/172.24  																																																																																																																																																																																																																	|
% 223.07/172.24  																																																																																																																																																																																																																	+-Applying beta-rule and splitting (659), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																	| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.07/172.24  																																																																																																																																																																																																																	|
% 223.07/172.24  																																																																																																																																																																																																																		| From (1281) and (2039) follows:
% 223.07/172.24  																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.24  																																																																																																																																																																																																																		|
% 223.07/172.24  																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.07/172.24  																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																		|
% 223.07/172.24  																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																	| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.07/172.24  																																																																																																																																																																																																																	| (2865) all_37_2_63 = all_12_0_10
% 223.07/172.24  																																																																																																																																																																																																																	|
% 223.07/172.24  																																																																																																																																																																																																																		| Combining equations (1195,2865) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 223.07/172.24  																																																																																																																																																																																																																		|
% 223.07/172.24  																																																																																																																																																																																																																		| From (1281) and (2042) follows:
% 223.07/172.24  																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.07/172.24  																																																																																																																																																																																																																		|
% 223.07/172.24  																																																																																																																																																																																																																		+-Applying beta-rule and splitting (423), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																		| (2883)  ~ (aNaturalNumber0(all_0_7_7) = all_20_2_24)
% 223.07/172.24  																																																																																																																																																																																																																		|
% 223.07/172.24  																																																																																																																																																																																																																			| From (1787) and (2883) follows:
% 223.07/172.24  																																																																																																																																																																																																																			| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																			| Using (1295) and (2129) yields:
% 223.07/172.24  																																																																																																																																																																																																																			| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																		|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																		| (2886) aNaturalNumber0(all_0_7_7) = all_20_2_24
% 223.07/172.24  																																																																																																																																																																																																																		| (2887) all_20_2_24 = all_16_0_16
% 223.07/172.24  																																																																																																																																																																																																																		|
% 223.07/172.24  																																																																																																																																																																																																																			| Combining equations (2887,1787) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																			| (2760) all_16_0_16 = 0
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																			| Simplifying 2760 yields:
% 223.07/172.24  																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																			| From (1787) and (2886) follows:
% 223.07/172.24  																																																																																																																																																																																																																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																			+-Applying beta-rule and splitting (673), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																			|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																			| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																				| From (1292) and (2023) follows:
% 223.07/172.24  																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.24  																																																																																																																																																																																																																				|
% 223.07/172.24  																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.07/172.24  																																																																																																																																																																																																																				| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																				|
% 223.07/172.24  																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																			|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																			| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.07/172.24  																																																																																																																																																																																																																			| (2880) all_26_1_32 = all_16_0_16
% 223.07/172.24  																																																																																																																																																																																																																			|
% 223.07/172.24  																																																																																																																																																																																																																				| Combining equations (1202,2880) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 223.07/172.24  																																																																																																																																																																																																																				|
% 223.07/172.24  																																																																																																																																																																																																																				| From (1292) and (2026) follows:
% 223.07/172.24  																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.07/172.24  																																																																																																																																																																																																																				|
% 223.07/172.24  																																																																																																																																																																																																																				+-Applying beta-rule and splitting (641), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																				|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																				| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.07/172.24  																																																																																																																																																																																																																				|
% 223.07/172.24  																																																																																																																																																																																																																					| From (1350) and (2899) follows:
% 223.07/172.24  																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.07/172.24  																																																																																																																																																																																																																					| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																				|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																				| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.07/172.24  																																																																																																																																																																																																																				| (2903) all_39_6_72 = all_24_0_28
% 223.07/172.24  																																																																																																																																																																																																																				|
% 223.07/172.24  																																																																																																																																																																																																																					| Combining equations (2903,629) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																					| (5715) all_24_0_28 = 0
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																					| Simplifying 5715 yields:
% 223.07/172.24  																																																																																																																																																																																																																					| (1350) all_24_0_28 = 0
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																					| From (1350) and (2902) follows:
% 223.07/172.24  																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1097), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																					|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																					| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																						| From (1229) and (2891) follows:
% 223.07/172.24  																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.24  																																																																																																																																																																																																																						|
% 223.07/172.24  																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.07/172.24  																																																																																																																																																																																																																						| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																						|
% 223.07/172.24  																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																					|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																					| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.07/172.24  																																																																																																																																																																																																																					| (2895) all_22_1_26 = all_16_2_18
% 223.07/172.24  																																																																																																																																																																																																																					|
% 223.07/172.24  																																																																																																																																																																																																																						| From (1229) and (2894) follows:
% 223.07/172.24  																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.07/172.24  																																																																																																																																																																																																																						|
% 223.07/172.24  																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1116), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																						|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																						| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.07/172.24  																																																																																																																																																																																																																						|
% 223.07/172.24  																																																																																																																																																																																																																							| From (1674) and (2552) follows:
% 223.07/172.24  																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.07/172.24  																																																																																																																																																																																																																							| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																						|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																						| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.07/172.24  																																																																																																																																																																																																																						| (2918) all_52_2_87 = all_14_2_15
% 223.07/172.24  																																																																																																																																																																																																																						|
% 223.07/172.24  																																																																																																																																																																																																																							| Combining equations (1674,2918) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																							| (1200) all_14_2_15 = 0
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																							| Combining equations (1200,2918) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																							| (1674) all_52_2_87 = 0
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																							| From (1674) and (2555) follows:
% 223.07/172.24  																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1092), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																							|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																							| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																								| From (1244) and (2604) follows:
% 223.07/172.24  																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.07/172.24  																																																																																																																																																																																																																								| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																							|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																							| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.07/172.24  																																																																																																																																																																																																																							| (2910) all_72_1_100 = all_16_2_18
% 223.07/172.24  																																																																																																																																																																																																																							|
% 223.07/172.24  																																																																																																																																																																																																																								| Combining equations (1244,2910) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																								| (1225) all_16_2_18 = 0
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																								| Combining equations (1225,2910) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																								| (1244) all_72_1_100 = 0
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																								| From (1244) and (2607) follows:
% 223.07/172.24  																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																								+-Applying beta-rule and splitting (776), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																								|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																								| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																									| From (1791) and (1977) follows:
% 223.07/172.24  																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.07/172.24  																																																																																																																																																																																																																									| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																								|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																								| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.07/172.24  																																																																																																																																																																																																																								| (2934) all_72_2_101 = all_37_3_64
% 223.07/172.24  																																																																																																																																																																																																																								|
% 223.07/172.24  																																																																																																																																																																																																																									| Combining equations (1791,2934) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																									| (1233) all_37_3_64 = 0
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																									| Combining equations (1233,2934) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																									| From (1791) and (1980) follows:
% 223.07/172.24  																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																									+-Applying beta-rule and splitting (730), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																									|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																									| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																										| From (1281) and (1969) follows:
% 223.07/172.24  																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.07/172.24  																																																																																																																																																																																																																										| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																									|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																									| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.07/172.24  																																																																																																																																																																																																																									| (2926) all_67_1_96 = all_12_0_10
% 223.07/172.24  																																																																																																																																																																																																																									|
% 223.07/172.24  																																																																																																																																																																																																																										| Combining equations (1242,2926) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																										| (1281) all_12_0_10 = 0
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																										| Combining equations (1281,2926) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																										| (1242) all_67_1_96 = 0
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																										| From (1281) and (1972) follows:
% 223.07/172.24  																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																										+-Applying beta-rule and splitting (600), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																										|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																										| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																											| From (1791) and (2642) follows:
% 223.07/172.24  																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.07/172.24  																																																																																																																																																																																																																											| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																										|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																										| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.07/172.24  																																																																																																																																																																																																																										| (2950) all_72_2_101 = all_52_1_86
% 223.07/172.24  																																																																																																																																																																																																																										|
% 223.07/172.24  																																																																																																																																																																																																																											| Combining equations (1791,2950) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																											| (1238) all_52_1_86 = 0
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																											| Combining equations (1238,2950) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																											| (1791) all_72_2_101 = 0
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																											| From (1791) and (2645) follows:
% 223.07/172.24  																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																											+-Applying beta-rule and splitting (708), into two cases.
% 223.07/172.24  																																																																																																																																																																																																																											|-Branch one:
% 223.07/172.24  																																																																																																																																																																																																																											| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																												| From (1350) and (2136) follows:
% 223.07/172.24  																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.24  																																																																																																																																																																																																																												|
% 223.07/172.24  																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.07/172.24  																																																																																																																																																																																																																												| (1311) $false
% 223.07/172.24  																																																																																																																																																																																																																												|
% 223.07/172.24  																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.24  																																																																																																																																																																																																																											|-Branch two:
% 223.07/172.24  																																																																																																																																																																																																																											| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.07/172.24  																																																																																																																																																																																																																											| (2942) all_72_1_100 = all_24_0_28
% 223.07/172.24  																																																																																																																																																																																																																											|
% 223.07/172.24  																																																																																																																																																																																																																												| Combining equations (1244,2942) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 223.07/172.24  																																																																																																																																																																																																																												|
% 223.07/172.24  																																																																																																																																																																																																																												| Combining equations (1350,2942) yields a new equation:
% 223.07/172.24  																																																																																																																																																																																																																												| (1244) all_72_1_100 = 0
% 223.07/172.24  																																																																																																																																																																																																																												|
% 223.07/172.24  																																																																																																																																																																																																																												| From (1350) and (2139) follows:
% 223.07/172.25  																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.07/172.25  																																																																																																																																																																																																																												|
% 223.07/172.25  																																																																																																																																																																																																																												+-Applying beta-rule and splitting (804), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																												|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																												| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.07/172.25  																																																																																																																																																																																																																												|
% 223.07/172.25  																																																																																																																																																																																																																													| From (1293) and (2962) follows:
% 223.07/172.25  																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.07/172.25  																																																																																																																																																																																																																													| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																												|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																												| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.07/172.25  																																																																																																																																																																																																																												| (2966) all_47_2_83 = all_22_1_26
% 223.07/172.25  																																																																																																																																																																																																																												|
% 223.07/172.25  																																																																																																																																																																																																																													| Combining equations (1293,2966) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																													| (1229) all_22_1_26 = 0
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																													| Combining equations (1229,2966) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																													| (1293) all_47_2_83 = 0
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																													| From (1293) and (2965) follows:
% 223.07/172.25  																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1115), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																													|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																													| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																														| From (1281) and (2374) follows:
% 223.07/172.25  																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.25  																																																																																																																																																																																																																														|
% 223.07/172.25  																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.07/172.25  																																																																																																																																																																																																																														| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																														|
% 223.07/172.25  																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																													|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																													| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.07/172.25  																																																																																																																																																																																																																													| (2958) all_14_2_15 = all_12_0_10
% 223.07/172.25  																																																																																																																																																																																																																													|
% 223.07/172.25  																																																																																																																																																																																																																														| Combining equations (1200,2958) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 223.07/172.25  																																																																																																																																																																																																																														|
% 223.07/172.25  																																																																																																																																																																																																																														| From (1281) and (2377) follows:
% 223.07/172.25  																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.07/172.25  																																																																																																																																																																																																																														|
% 223.07/172.25  																																																																																																																																																																																																																														+-Applying beta-rule and splitting (490), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																														|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																														| (2178)  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 223.07/172.25  																																																																																																																																																																																																																														|
% 223.07/172.25  																																																																																																																																																																																																																															| From (1828) and (2178) follows:
% 223.07/172.25  																																																																																																																																																																																																																															| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																															| Using (1284) and (2090) yields:
% 223.07/172.25  																																																																																																																																																																																																																															| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																														|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																														| (2181) aNaturalNumber0(all_0_9_9) = all_20_0_22
% 223.07/172.25  																																																																																																																																																																																																																														| (2980) all_20_0_22 = all_12_0_10
% 223.07/172.25  																																																																																																																																																																																																																														|
% 223.07/172.25  																																																																																																																																																																																																																															| Combining equations (2980,1828) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																															| (2959) all_12_0_10 = 0
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																															| Simplifying 2959 yields:
% 223.07/172.25  																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																															| From (1828) and (2181) follows:
% 223.07/172.25  																																																																																																																																																																																																																															| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1152), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																															|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																															| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																																| From (1221) and (2081) follows:
% 223.07/172.25  																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																|
% 223.07/172.25  																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.07/172.25  																																																																																																																																																																																																																																| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																|
% 223.07/172.25  																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																															|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																															| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.07/172.25  																																																																																																																																																																																																																															| (2974) all_12_1_11 = all_12_2_12
% 223.07/172.25  																																																																																																																																																																																																																															|
% 223.07/172.25  																																																																																																																																																																																																																																| From (1221) and (2084) follows:
% 223.07/172.25  																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.07/172.25  																																																																																																																																																																																																																																|
% 223.07/172.25  																																																																																																																																																																																																																																+-Applying beta-rule and splitting (601), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.07/172.25  																																																																																																																																																																																																																																|
% 223.07/172.25  																																																																																																																																																																																																																																	| From (1790) and (2506) follows:
% 223.07/172.25  																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.07/172.25  																																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.07/172.25  																																																																																																																																																																																																																																| (2996) all_62_2_94 = all_52_1_86
% 223.07/172.25  																																																																																																																																																																																																																																|
% 223.07/172.25  																																																																																																																																																																																																																																	| Combining equations (1790,2996) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																	| (1238) all_52_1_86 = 0
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																	| Combining equations (1238,2996) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																	| (1790) all_62_2_94 = 0
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																	| From (1790) and (2509) follows:
% 223.07/172.25  																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1136), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																	| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																		| From (1292) and (2984) follows:
% 223.07/172.25  																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.07/172.25  																																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																	| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.07/172.25  																																																																																																																																																																																																																																	| (2988) all_16_0_16 = all_12_2_12
% 223.07/172.25  																																																																																																																																																																																																																																	|
% 223.07/172.25  																																																																																																																																																																																																																																		| Combining equations (1292,2988) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																		| (1223) all_12_2_12 = 0
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																		| Combining equations (1223,2988) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																		| From (1292) and (2987) follows:
% 223.07/172.25  																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (966), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																		| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																			| From (1282) and (2210) follows:
% 223.07/172.25  																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.07/172.25  																																																																																																																																																																																																																																			| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																		|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																		| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.07/172.25  																																																																																																																																																																																																																																		| (3012) all_62_1_93 = all_24_2_30
% 223.07/172.25  																																																																																																																																																																																																																																		|
% 223.07/172.25  																																																																																																																																																																																																																																			| Combining equations (1240,3012) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																			| (1282) all_24_2_30 = 0
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																			| Combining equations (1282,3012) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																			| (1240) all_62_1_93 = 0
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																			| From (1282) and (2213) follows:
% 223.07/172.25  																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1069), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																			|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																			| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																				| From (1237) and (2490) follows:
% 223.07/172.25  																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.07/172.25  																																																																																																																																																																																																																																				| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																			|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																			| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.07/172.25  																																																																																																																																																																																																																																			| (3004) all_47_1_82 = all_18_2_21
% 223.07/172.25  																																																																																																																																																																																																																																			|
% 223.07/172.25  																																																																																																																																																																																																																																				| Combining equations (1237,3004) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																				| (1226) all_18_2_21 = 0
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																				| Combining equations (1226,3004) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																				| (1237) all_47_1_82 = 0
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																				| From (1237) and (2493) follows:
% 223.07/172.25  																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (849), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																				|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																				| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																					| From (848) and (2268) follows:
% 223.07/172.25  																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																					|
% 223.07/172.25  																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.07/172.25  																																																																																																																																																																																																																																					| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																					|
% 223.07/172.25  																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																				|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																				| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.07/172.25  																																																																																																																																																																																																																																				| (848) all_16_1_17 = 0
% 223.07/172.25  																																																																																																																																																																																																																																				|
% 223.07/172.25  																																																																																																																																																																																																																																					| From (848) and (2271) follows:
% 223.07/172.25  																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.07/172.25  																																																																																																																																																																																																																																					|
% 223.07/172.25  																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1080), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																					|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																					| (3016)  ~ (aNaturalNumber0(sz00) = all_16_2_18)
% 223.07/172.25  																																																																																																																																																																																																																																					|
% 223.07/172.25  																																																																																																																																																																																																																																						| From (1225) and (3016) follows:
% 223.07/172.25  																																																																																																																																																																																																																																						| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																						|
% 223.07/172.25  																																																																																																																																																																																																																																						| Using (26) and (2070) yields:
% 223.07/172.25  																																																																																																																																																																																																																																						| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																						|
% 223.07/172.25  																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																					|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																					| (3019) aNaturalNumber0(sz00) = all_16_2_18
% 223.07/172.25  																																																																																																																																																																																																																																					| (1225) all_16_2_18 = 0
% 223.07/172.25  																																																																																																																																																																																																																																					|
% 223.07/172.25  																																																																																																																																																																																																																																						| From (1225) and (3019) follows:
% 223.07/172.25  																																																																																																																																																																																																																																						| (26) aNaturalNumber0(sz00) = 0
% 223.07/172.25  																																																																																																																																																																																																																																						|
% 223.07/172.25  																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (788), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																						|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																						| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.07/172.25  																																																																																																																																																																																																																																						|
% 223.07/172.25  																																																																																																																																																																																																																																							| From (1674) and (3035) follows:
% 223.07/172.25  																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.07/172.25  																																																																																																																																																																																																																																							| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																						|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																						| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.07/172.25  																																																																																																																																																																																																																																						| (3039) all_52_2_87 = all_37_3_64
% 223.07/172.25  																																																																																																																																																																																																																																						|
% 223.07/172.25  																																																																																																																																																																																																																																							| Combining equations (1674,3039) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																							| (1233) all_37_3_64 = 0
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																							| Combining equations (1233,3039) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																							| (1674) all_52_2_87 = 0
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																							| From (1674) and (3038) follows:
% 223.07/172.25  																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (785), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																							|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																							| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																								| From (1283) and (3028) follows:
% 223.07/172.25  																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																								|
% 223.07/172.25  																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.07/172.25  																																																																																																																																																																																																																																								| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																								|
% 223.07/172.25  																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																							|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																							| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.07/172.25  																																																																																																																																																																																																																																							| (3032) all_37_3_64 = all_26_2_33
% 223.07/172.25  																																																																																																																																																																																																																																							|
% 223.07/172.25  																																																																																																																																																																																																																																								| Combining equations (1233,3032) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																								| (1283) all_26_2_33 = 0
% 223.07/172.25  																																																																																																																																																																																																																																								|
% 223.07/172.25  																																																																																																																																																																																																																																								| Combining equations (1283,3032) yields a new equation:
% 223.07/172.25  																																																																																																																																																																																																																																								| (1233) all_37_3_64 = 0
% 223.07/172.25  																																																																																																																																																																																																																																								|
% 223.07/172.25  																																																																																																																																																																																																																																								| From (1283) and (3031) follows:
% 223.07/172.25  																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.07/172.25  																																																																																																																																																																																																																																								|
% 223.07/172.25  																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (405), into two cases.
% 223.07/172.25  																																																																																																																																																																																																																																								|-Branch one:
% 223.07/172.25  																																																																																																																																																																																																																																								| (2755)  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 223.07/172.25  																																																																																																																																																																																																																																								|
% 223.07/172.25  																																																																																																																																																																																																																																									| From (1790) and (2755) follows:
% 223.07/172.25  																																																																																																																																																																																																																																									| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.07/172.25  																																																																																																																																																																																																																																									|
% 223.07/172.25  																																																																																																																																																																																																																																									| Using (1295) and (2129) yields:
% 223.07/172.25  																																																																																																																																																																																																																																									| (1311) $false
% 223.07/172.25  																																																																																																																																																																																																																																									|
% 223.07/172.25  																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.25  																																																																																																																																																																																																																																								|-Branch two:
% 223.07/172.25  																																																																																																																																																																																																																																								| (2758) aNaturalNumber0(all_0_7_7) = all_62_2_94
% 223.07/172.25  																																																																																																																																																																																																																																								| (3055) all_62_2_94 = all_47_2_83
% 223.07/172.26  																																																																																																																																																																																																																																								|
% 223.07/172.26  																																																																																																																																																																																																																																									| Combining equations (1790,3055) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																									| (1293) all_47_2_83 = 0
% 223.07/172.26  																																																																																																																																																																																																																																									|
% 223.07/172.26  																																																																																																																																																																																																																																									| Combining equations (1293,3055) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																									| (1790) all_62_2_94 = 0
% 223.07/172.26  																																																																																																																																																																																																																																									|
% 223.07/172.26  																																																																																																																																																																																																																																									| From (1790) and (2758) follows:
% 223.07/172.26  																																																																																																																																																																																																																																									| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.07/172.26  																																																																																																																																																																																																																																									|
% 223.07/172.26  																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (946), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																									|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																									| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.07/172.26  																																																																																																																																																																																																																																									|
% 223.07/172.26  																																																																																																																																																																																																																																										| From (1242) and (2334) follows:
% 223.07/172.26  																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																										| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																									|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																									| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.07/172.26  																																																																																																																																																																																																																																									| (3047) all_77_1_104 = all_67_1_96
% 223.07/172.26  																																																																																																																																																																																																																																									|
% 223.07/172.26  																																																																																																																																																																																																																																										| Combining equations (1246,3047) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																										| (1242) all_67_1_96 = 0
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																										| Combining equations (1242,3047) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																										| (1246) all_77_1_104 = 0
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																										| From (1242) and (2337) follows:
% 223.07/172.26  																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1139), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																										|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																										| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																											| From (1282) and (2210) follows:
% 223.07/172.26  																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																											| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																										|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																										| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.07/172.26  																																																																																																																																																																																																																																										| (3071) all_24_2_30 = all_12_2_12
% 223.07/172.26  																																																																																																																																																																																																																																										|
% 223.07/172.26  																																																																																																																																																																																																																																											| Combining equations (1282,3071) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																											| (1223) all_12_2_12 = 0
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																											| Combining equations (1223,3071) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																											| From (1282) and (2213) follows:
% 223.07/172.26  																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (952), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																											|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																											| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																												| From (848) and (2268) follows:
% 223.07/172.26  																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																												| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																											|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																											| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.07/172.26  																																																																																																																																																																																																																																											| (3063) all_77_1_104 = all_16_1_17
% 223.07/172.26  																																																																																																																																																																																																																																											|
% 223.07/172.26  																																																																																																																																																																																																																																												| Combining equations (1246,3063) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																												| (848) all_16_1_17 = 0
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																												| Combining equations (848,3063) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																												| (1246) all_77_1_104 = 0
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																												| From (848) and (2271) follows:
% 223.07/172.26  																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1148), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																												|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																												| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																													| From (1228) and (2055) follows:
% 223.07/172.26  																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																													| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																												|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																												| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.07/172.26  																																																																																																																																																																																																																																												| (3087) all_20_1_23 = all_12_2_12
% 223.07/172.26  																																																																																																																																																																																																																																												|
% 223.07/172.26  																																																																																																																																																																																																																																													| Combining equations (1228,3087) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																													| (1223) all_12_2_12 = 0
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																													| Combining equations (1223,3087) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																													| (1228) all_20_1_23 = 0
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																													| From (1228) and (2058) follows:
% 223.07/172.26  																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (937), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																													|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																													| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																														| From (1294) and (1953) follows:
% 223.07/172.26  																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																														| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																													|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																													| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.07/172.26  																																																																																																																																																																																																																																													| (3079) all_77_1_104 = all_77_2_105
% 223.07/172.26  																																																																																																																																																																																																																																													|
% 223.07/172.26  																																																																																																																																																																																																																																														| Combining equations (1246,3079) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																														| Combining equations (1294,3079) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																														| (1246) all_77_1_104 = 0
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																														| From (1294) and (1956) follows:
% 223.07/172.26  																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (594), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																														|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																														| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																															| From (1283) and (2007) follows:
% 223.07/172.26  																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																															|
% 223.07/172.26  																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 223.07/172.26  																																																																																																																																																																																																																																															| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																															|
% 223.07/172.26  																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																														|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																														| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.07/172.26  																																																																																																																																																																																																																																														| (3103) all_57_3_91 = all_26_2_33
% 223.07/172.26  																																																																																																																																																																																																																																														|
% 223.07/172.26  																																																																																																																																																																																																																																															| Combining equations (2199,3103) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																															| (1283) all_26_2_33 = 0
% 223.07/172.26  																																																																																																																																																																																																																																															|
% 223.07/172.26  																																																																																																																																																																																																																																															| From (1283) and (2010) follows:
% 223.07/172.26  																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 223.07/172.26  																																																																																																																																																																																																																																															|
% 223.07/172.26  																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1040), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																															|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																															| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.07/172.26  																																																																																																																																																																																																																																															|
% 223.07/172.26  																																																																																																																																																																																																																																																| From (1282) and (2210) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																																| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																															|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																															| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.07/172.26  																																																																																																																																																																																																																																															| (3095) all_37_4_65 = all_24_2_30
% 223.07/172.26  																																																																																																																																																																																																																																															|
% 223.07/172.26  																																																																																																																																																																																																																																																| Combining equations (1232,3095) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																| (1282) all_24_2_30 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																| Combining equations (1282,3095) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																| (1232) all_37_4_65 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																| From (1282) and (2213) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (901), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																																|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																																| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																	| From (1293) and (2962) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																																|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																																| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.07/172.26  																																																																																																																																																																																																																																																| (3116) all_47_2_83 = all_12_1_11
% 223.07/172.26  																																																																																																																																																																																																																																																|
% 223.07/172.26  																																																																																																																																																																																																																																																	| Combining equations (1293,3116) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (1221) all_12_1_11 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																	| Combining equations (1221,3116) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																	| From (1293) and (2965) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (753), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (3106)  ~ (aNaturalNumber0(sz00) = all_39_7_73)
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																		| From (1236) and (3106) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																		| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																																		|
% 223.07/172.26  																																																																																																																																																																																																																																																		| Using (26) and (2070) yields:
% 223.07/172.26  																																																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																																		|
% 223.07/172.26  																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																																	| (3109) aNaturalNumber0(sz00) = all_39_7_73
% 223.07/172.26  																																																																																																																																																																																																																																																	| (1236) all_39_7_73 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																	|
% 223.07/172.26  																																																																																																																																																																																																																																																		| From (1236) and (3109) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																		| (26) aNaturalNumber0(sz00) = 0
% 223.07/172.26  																																																																																																																																																																																																																																																		|
% 223.07/172.26  																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (844), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																																		| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.07/172.26  																																																																																																																																																																																																																																																		|
% 223.07/172.26  																																																																																																																																																																																																																																																			| From (1282) and (2382) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																																		|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																																		| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.07/172.26  																																																																																																																																																																																																																																																		| (3132) all_24_2_30 = all_18_1_20
% 223.07/172.26  																																																																																																																																																																																																																																																		|
% 223.07/172.26  																																																																																																																																																																																																																																																			| Combining equations (1282,3132) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (1227) all_18_1_20 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																			| Combining equations (1227,3132) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (1282) all_24_2_30 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																			| From (1282) and (2385) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1086), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																																			|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																				| From (1292) and (2984) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																																			|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																																			| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.07/172.26  																																																																																																																																																																																																																																																			| (3124) all_16_0_16 = all_16_2_18
% 223.07/172.26  																																																																																																																																																																																																																																																			|
% 223.07/172.26  																																																																																																																																																																																																																																																				| Combining equations (1292,3124) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (1225) all_16_2_18 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																				| Combining equations (1225,3124) yields a new equation:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																				| From (1292) and (2987) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (353), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																																				|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (3144)  ~ (aNaturalNumber0(sz00) = all_57_2_90)
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																					| From (1789) and (3144) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																					| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.07/172.26  																																																																																																																																																																																																																																																					|
% 223.07/172.26  																																																																																																																																																																																																																																																					| Using (26) and (2070) yields:
% 223.07/172.26  																																																																																																																																																																																																																																																					| (1311) $false
% 223.07/172.26  																																																																																																																																																																																																																																																					|
% 223.07/172.26  																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.07/172.26  																																																																																																																																																																																																																																																				|-Branch two:
% 223.07/172.26  																																																																																																																																																																																																																																																				| (3147) aNaturalNumber0(sz00) = all_57_2_90
% 223.07/172.26  																																																																																																																																																																																																																																																				| (1789) all_57_2_90 = 0
% 223.07/172.26  																																																																																																																																																																																																																																																				|
% 223.07/172.26  																																																																																																																																																																																																																																																					| From (1789) and (3147) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																					| (26) aNaturalNumber0(sz00) = 0
% 223.07/172.26  																																																																																																																																																																																																																																																					|
% 223.07/172.26  																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1060), into two cases.
% 223.07/172.26  																																																																																																																																																																																																																																																					|-Branch one:
% 223.07/172.26  																																																																																																																																																																																																																																																					| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.07/172.26  																																																																																																																																																																																																																																																					|
% 223.07/172.26  																																																																																																																																																																																																																																																						| From (1294) and (1953) follows:
% 223.07/172.26  																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																						| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																					|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																					| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.07/172.27  																																																																																																																																																																																																																																																					| (3140) all_77_2_105 = all_18_2_21
% 223.07/172.27  																																																																																																																																																																																																																																																					|
% 223.07/172.27  																																																																																																																																																																																																																																																						| Combining equations (1294,3140) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																						| (1226) all_18_2_21 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																						| Combining equations (1226,3140) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																						| From (1294) and (1956) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (458), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																						|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																						| (2467)  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																							| From (1293) and (2467) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																							| Using (1284) and (2090) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																						|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																						| (2470) aNaturalNumber0(all_0_9_9) = all_47_2_83
% 223.07/172.27  																																																																																																																																																																																																																																																						| (3161) all_47_2_83 = all_26_2_33
% 223.07/172.27  																																																																																																																																																																																																																																																						|
% 223.07/172.27  																																																																																																																																																																																																																																																							| Combining equations (1293,3161) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																							| Combining equations (1283,3161) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (1293) all_47_2_83 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																							| From (1293) and (2470) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1037), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																							|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																								| From (1292) and (2984) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																								|
% 223.07/172.27  																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																								| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																								|
% 223.07/172.27  																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																							|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																							| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.07/172.27  																																																																																																																																																																																																																																																							| (3154) all_37_4_65 = all_16_0_16
% 223.07/172.27  																																																																																																																																																																																																																																																							|
% 223.07/172.27  																																																																																																																																																																																																																																																								| Combining equations (1232,3154) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																								| (1292) all_16_0_16 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																								|
% 223.07/172.27  																																																																																																																																																																																																																																																								| From (1292) and (2987) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																								|
% 223.07/172.27  																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (374), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																								|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																								| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																								|
% 223.07/172.27  																																																																																																																																																																																																																																																									| Using (1775) and (1780) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																									| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																									|
% 223.07/172.27  																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																								|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																								| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																								| (1787) all_20_2_24 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																								|
% 223.07/172.27  																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1028), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																									|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																									| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.07/172.27  																																																																																																																																																																																																																																																									|
% 223.07/172.27  																																																																																																																																																																																																																																																										| From (1218) and (3165) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																									|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																									| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.07/172.27  																																																																																																																																																																																																																																																									| (3169) all_39_8_74 = all_14_1_14
% 223.07/172.27  																																																																																																																																																																																																																																																									|
% 223.07/172.27  																																																																																																																																																																																																																																																										| Combining equations (1179,3169) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (1218) all_14_1_14 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																										| Combining equations (1218,3169) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (1179) all_39_8_74 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																										| From (1218) and (3168) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (461), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																										|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (3184)  ~ (aNaturalNumber0(xr) = all_24_2_30)
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																											| From (1282) and (3184) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																											| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																											|
% 223.07/172.27  																																																																																																																																																																																																																																																											| Using (88) and (8229) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																											| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																											|
% 223.07/172.27  																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																										|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																										| (3187) aNaturalNumber0(xr) = all_24_2_30
% 223.07/172.27  																																																																																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																										|
% 223.07/172.27  																																																																																																																																																																																																																																																											| From (1282) and (3187) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																											| (88) aNaturalNumber0(xr) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																											|
% 223.07/172.27  																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1024), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																											|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																											| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.07/172.27  																																																																																																																																																																																																																																																											|
% 223.07/172.27  																																																																																																																																																																																																																																																												| From (1229) and (2891) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																												|
% 223.07/172.27  																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																												| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																												|
% 223.07/172.27  																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																											|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																											| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.07/172.27  																																																																																																																																																																																																																																																											| (3181) all_39_8_74 = all_22_1_26
% 223.07/172.27  																																																																																																																																																																																																																																																											|
% 223.07/172.27  																																																																																																																																																																																																																																																												| Combining equations (1179,3181) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																												| (1229) all_22_1_26 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																												|
% 223.07/172.27  																																																																																																																																																																																																																																																												| From (1229) and (2894) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																												|
% 223.07/172.27  																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (968), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																												|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																												| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.07/172.27  																																																																																																																																																																																																																																																												|
% 223.07/172.27  																																																																																																																																																																																																																																																													| From (1674) and (2552) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																												|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																												| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.07/172.27  																																																																																																																																																																																																																																																												| (3202) all_62_1_93 = all_52_2_87
% 223.07/172.27  																																																																																																																																																																																																																																																												|
% 223.07/172.27  																																																																																																																																																																																																																																																													| Combining equations (1240,3202) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (1674) all_52_2_87 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																													| Combining equations (1674,3202) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (1240) all_62_1_93 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																													| From (1674) and (2555) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1012), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																													|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																														| From (1293) and (2061) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																													|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																													| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.07/172.27  																																																																																																																																																																																																																																																													| (3194) all_47_2_83 = all_39_8_74
% 223.07/172.27  																																																																																																																																																																																																																																																													|
% 223.07/172.27  																																																																																																																																																																																																																																																														| Combining equations (1293,3194) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (1179) all_39_8_74 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																														| Combining equations (1179,3194) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (1293) all_47_2_83 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																														| From (1293) and (2064) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (891), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																														|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (3214)  ~ (aNaturalNumber0(sz00) = all_12_1_11)
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																															| From (1221) and (3214) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																															| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																															|
% 223.07/172.27  																																																																																																																																																																																																																																																															| Using (26) and (2070) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																															| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																															|
% 223.07/172.27  																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																														|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																														| (3217) aNaturalNumber0(sz00) = all_12_1_11
% 223.07/172.27  																																																																																																																																																																																																																																																														| (1221) all_12_1_11 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																														|
% 223.07/172.27  																																																																																																																																																																																																																																																															| From (1221) and (3217) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																															| (26) aNaturalNumber0(sz00) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																															|
% 223.07/172.27  																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (991), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																															|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																															| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.07/172.27  																																																																																																																																																																																																																																																															|
% 223.07/172.27  																																																																																																																																																																																																																																																																| From (1282) and (2210) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																															|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																															| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.07/172.27  																																																																																																																																																																																																																																																															| (3210) all_57_1_89 = all_24_2_30
% 223.07/172.27  																																																																																																																																																																																																																																																															|
% 223.07/172.27  																																																																																																																																																																																																																																																																| Combining equations (980,3210) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (1282) all_24_2_30 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																| Combining equations (1282,3210) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (980) all_57_1_89 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																| From (1282) and (2213) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (562), into two cases.
% 223.07/172.27  																																																																																																																																																																																																																																																																|-Branch one:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																	| From (1283) and (2007) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.27  																																																																																																																																																																																																																																																																	|
% 223.07/172.27  																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.07/172.27  																																																																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.27  																																																																																																																																																																																																																																																																	|
% 223.07/172.27  																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.27  																																																																																																																																																																																																																																																																|-Branch two:
% 223.07/172.27  																																																																																																																																																																																																																																																																| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.07/172.27  																																																																																																																																																																																																																																																																| (3231) all_72_3_102 = all_26_2_33
% 223.07/172.27  																																																																																																																																																																																																																																																																|
% 223.07/172.27  																																																																																																																																																																																																																																																																	| Combining equations (1243,3231) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																																	| (1283) all_26_2_33 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																																	|
% 223.07/172.27  																																																																																																																																																																																																																																																																	| Combining equations (1283,3231) yields a new equation:
% 223.07/172.27  																																																																																																																																																																																																																																																																	| (1243) all_72_3_102 = 0
% 223.07/172.27  																																																																																																																																																																																																																																																																	|
% 223.07/172.27  																																																																																																																																																																																																																																																																	| From (1283) and (2010) follows:
% 223.07/172.27  																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																	|
% 223.07/172.28  																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (988), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																	| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.07/172.28  																																																																																																																																																																																																																																																																	|
% 223.07/172.28  																																																																																																																																																																																																																																																																		| From (1292) and (2984) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																		|
% 223.07/172.28  																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																		|
% 223.07/172.28  																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																	| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.07/172.28  																																																																																																																																																																																																																																																																	| (3224) all_57_1_89 = all_16_0_16
% 223.07/172.28  																																																																																																																																																																																																																																																																	|
% 223.07/172.28  																																																																																																																																																																																																																																																																		| Combining equations (980,3224) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																		|
% 223.07/172.28  																																																																																																																																																																																																																																																																		| From (1292) and (2987) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																		|
% 223.07/172.28  																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (443), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.07/172.28  																																																																																																																																																																																																																																																																		|
% 223.07/172.28  																																																																																																																																																																																																																																																																			| From (1283) and (2007) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																			|
% 223.07/172.28  																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																			| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																			|
% 223.07/172.28  																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																		|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.07/172.28  																																																																																																																																																																																																																																																																		| (1283) all_26_2_33 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																		|
% 223.07/172.28  																																																																																																																																																																																																																																																																			| From (1283) and (2010) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																			|
% 223.07/172.28  																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (749), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																			|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																			| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.07/172.28  																																																																																																																																																																																																																																																																			|
% 223.07/172.28  																																																																																																																																																																																																																																																																				| From (1281) and (1969) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																			|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																			| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.07/172.28  																																																																																																																																																																																																																																																																			| (3239) all_47_1_82 = all_12_0_10
% 223.07/172.28  																																																																																																																																																																																																																																																																			|
% 223.07/172.28  																																																																																																																																																																																																																																																																				| Combining equations (1237,3239) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (1281) all_12_0_10 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																				| Combining equations (1281,3239) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (1237) all_47_1_82 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																				| From (1281) and (1972) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (401), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																				|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (3255)  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																					| From (1830) and (3255) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																					| Using (1295) and (2129) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																				|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (3258) aNaturalNumber0(all_0_7_7) = all_82_2_109
% 223.07/172.28  																																																																																																																																																																																																																																																																				| (3259) all_82_2_109 = all_47_2_83
% 223.07/172.28  																																																																																																																																																																																																																																																																				|
% 223.07/172.28  																																																																																																																																																																																																																																																																					| Combining equations (1830,3259) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																					| Combining equations (1293,3259) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (1830) all_82_2_109 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																					| From (1830) and (3258) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (734), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																					|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (3249)  ~ (aNaturalNumber0(sz10) = all_47_1_82)
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																						| From (1237) and (3249) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																						| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																						|
% 223.07/172.28  																																																																																																																																																																																																																																																																						| Using (61) and (1994) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																						| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																						|
% 223.07/172.28  																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																					|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (3252) aNaturalNumber0(sz10) = all_47_1_82
% 223.07/172.28  																																																																																																																																																																																																																																																																					| (1237) all_47_1_82 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																					|
% 223.07/172.28  																																																																																																																																																																																																																																																																						| From (1237) and (3252) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																						| (61) aNaturalNumber0(sz10) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																						|
% 223.07/172.28  																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1151), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																						|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																						| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.07/172.28  																																																																																																																																																																																																																																																																						|
% 223.07/172.28  																																																																																																																																																																																																																																																																							| From (1218) and (3165) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																						|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																						| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.07/172.28  																																																																																																																																																																																																																																																																						| (3275) all_14_1_14 = all_12_2_12
% 223.07/172.28  																																																																																																																																																																																																																																																																						|
% 223.07/172.28  																																																																																																																																																																																																																																																																							| Combining equations (1218,3275) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (1223) all_12_2_12 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																							| Combining equations (1223,3275) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (1218) all_14_1_14 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																							| From (1218) and (3168) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (548), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																							|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																								| From (1281) and (2039) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																							|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.07/172.28  																																																																																																																																																																																																																																																																							| (3267) all_77_3_106 = all_12_0_10
% 223.07/172.28  																																																																																																																																																																																																																																																																							|
% 223.07/172.28  																																																																																																																																																																																																																																																																								| Combining equations (1245,3267) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (1281) all_12_0_10 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																								| Combining equations (1281,3267) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (1245) all_77_3_106 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																								| From (1281) and (2042) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1120), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																								|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																									| From (1236) and (2522) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																								|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.07/172.28  																																																																																																																																																																																																																																																																								| (3291) all_39_7_73 = all_14_2_15
% 223.07/172.28  																																																																																																																																																																																																																																																																								|
% 223.07/172.28  																																																																																																																																																																																																																																																																									| Combining equations (1236,3291) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (1200) all_14_2_15 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																									| Combining equations (1200,3291) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (1236) all_39_7_73 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																									| From (1236) and (2525) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1127), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																									|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																										| From (1221) and (2081) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																										|
% 223.07/172.28  																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																										|
% 223.07/172.28  																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																									|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.07/172.28  																																																																																																																																																																																																																																																																									| (3283) all_14_2_15 = all_12_1_11
% 223.07/172.28  																																																																																																																																																																																																																																																																									|
% 223.07/172.28  																																																																																																																																																																																																																																																																										| Combining equations (1200,3283) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (1221) all_12_1_11 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																										|
% 223.07/172.28  																																																																																																																																																																																																																																																																										| From (1221) and (2084) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																										|
% 223.07/172.28  																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (692), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																										|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.07/172.28  																																																																																																																																																																																																																																																																										|
% 223.07/172.28  																																																																																																																																																																																																																																																																											| From (1282) and (2475) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																											|
% 223.07/172.28  																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																											|
% 223.07/172.28  																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																										|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.07/172.28  																																																																																																																																																																																																																																																																										| (3307) all_24_1_29 = all_24_2_30
% 223.07/172.28  																																																																																																																																																																																																																																																																										|
% 223.07/172.28  																																																																																																																																																																																																																																																																											| Combining equations (1207,3307) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (1282) all_24_2_30 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																											|
% 223.07/172.28  																																																																																																																																																																																																																																																																											| From (1282) and (2478) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																											|
% 223.07/172.28  																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (925), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																											|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.07/172.28  																																																																																																																																																																																																																																																																											|
% 223.07/172.28  																																																																																																																																																																																																																																																																												| From (1233) and (3295) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																											|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.07/172.28  																																																																																																																																																																																																																																																																											| (3299) all_82_1_108 = all_37_3_64
% 223.07/172.28  																																																																																																																																																																																																																																																																											|
% 223.07/172.28  																																																																																																																																																																																																																																																																												| Combining equations (1249,3299) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (1233) all_37_3_64 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																												| Combining equations (1233,3299) yields a new equation:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (1249) all_82_1_108 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																												| From (1233) and (3298) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1129), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																												|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (3318)  ~ (aNaturalNumber0(sz10) = all_12_2_12)
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																													| From (1223) and (3318) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																													| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																													|
% 223.07/172.28  																																																																																																																																																																																																																																																																													| Using (61) and (1994) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																													| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																													|
% 223.07/172.28  																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																												|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (3321) aNaturalNumber0(sz10) = all_12_2_12
% 223.07/172.28  																																																																																																																																																																																																																																																																												| (1223) all_12_2_12 = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																												|
% 223.07/172.28  																																																																																																																																																																																																																																																																													| From (1223) and (3321) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																													| (61) aNaturalNumber0(sz10) = 0
% 223.07/172.28  																																																																																																																																																																																																																																																																													|
% 223.07/172.28  																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (639), into two cases.
% 223.07/172.28  																																																																																																																																																																																																																																																																													|-Branch one:
% 223.07/172.28  																																																																																																																																																																																																																																																																													| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.07/172.28  																																																																																																																																																																																																																																																																													|
% 223.07/172.28  																																																																																																																																																																																																																																																																														| From (1293) and (2159) follows:
% 223.07/172.28  																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.28  																																																																																																																																																																																																																																																																														|
% 223.07/172.28  																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 223.07/172.28  																																																																																																																																																																																																																																																																														| (1311) $false
% 223.07/172.28  																																																																																																																																																																																																																																																																														|
% 223.07/172.28  																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.28  																																																																																																																																																																																																																																																																													|-Branch two:
% 223.07/172.28  																																																																																																																																																																																																																																																																													| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.07/172.28  																																																																																																																																																																																																																																																																													| (3314) all_47_2_83 = all_39_6_72
% 223.07/172.28  																																																																																																																																																																																																																																																																													|
% 223.07/172.28  																																																																																																																																																																																																																																																																														| Combining equations (1293,3314) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																														| (629) all_39_6_72 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																														|
% 223.07/172.29  																																																																																																																																																																																																																																																																														| Combining equations (629,3314) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																														| (1293) all_47_2_83 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																														|
% 223.07/172.29  																																																																																																																																																																																																																																																																														| From (1293) and (2162) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																														|
% 223.07/172.29  																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (513), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																														|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																														| (3331)  ~ (aNaturalNumber0(xk) = all_47_2_83)
% 223.07/172.29  																																																																																																																																																																																																																																																																														|
% 223.07/172.29  																																																																																																																																																																																																																																																																															| From (1293) and (3331) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																															|
% 223.07/172.29  																																																																																																																																																																																																																																																																															| Using (1665) and (1670) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																															|
% 223.07/172.29  																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																														|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																														| (3334) aNaturalNumber0(xk) = all_47_2_83
% 223.07/172.29  																																																																																																																																																																																																																																																																														| (3335) all_52_2_87 = all_47_2_83
% 223.07/172.29  																																																																																																																																																																																																																																																																														|
% 223.07/172.29  																																																																																																																																																																																																																																																																															| Combining equations (1674,3335) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (1293) all_47_2_83 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																															|
% 223.07/172.29  																																																																																																																																																																																																																																																																															| From (1293) and (3334) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (1665) aNaturalNumber0(xk) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																															|
% 223.07/172.29  																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (963), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																															|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.07/172.29  																																																																																																																																																																																																																																																																															|
% 223.07/172.29  																																																																																																																																																																																																																																																																																| From (1292) and (2984) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																|
% 223.07/172.29  																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																|
% 223.07/172.29  																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																															|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.07/172.29  																																																																																																																																																																																																																																																																															| (3328) all_62_1_93 = all_16_0_16
% 223.07/172.29  																																																																																																																																																																																																																																																																															|
% 223.07/172.29  																																																																																																																																																																																																																																																																																| Combining equations (1240,3328) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (1292) all_16_0_16 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																|
% 223.07/172.29  																																																																																																																																																																																																																																																																																| From (1292) and (2987) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																|
% 223.07/172.29  																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (499), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (2232)  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 223.07/172.29  																																																																																																																																																																																																																																																																																|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| From (1350) and (2232) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| Using (1284) and (2090) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (2235) aNaturalNumber0(all_0_9_9) = all_24_0_28
% 223.07/172.29  																																																																																																																																																																																																																																																																																| (3351) all_24_0_28 = all_12_0_10
% 223.07/172.29  																																																																																																																																																																																																																																																																																|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| Combining equations (3351,1350) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (2959) all_12_0_10 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| Simplifying 2959 yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| From (1350) and (2235) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (653), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| From (1294) and (3339) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.07/172.29  																																																																																																																																																																																																																																																																																	| (3343) all_77_2_105 = all_37_2_63
% 223.07/172.29  																																																																																																																																																																																																																																																																																	|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| Combining equations (1294,3343) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (1195) all_37_2_63 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| Combining equations (1195,3343) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (1294) all_77_2_105 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| From (1294) and (3342) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (970), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| From (1242) and (2334) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.07/172.29  																																																																																																																																																																																																																																																																																		| (3367) all_67_1_96 = all_62_1_93
% 223.07/172.29  																																																																																																																																																																																																																																																																																		|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| Combining equations (1242,3367) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (1240) all_62_1_93 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| Combining equations (1240,3367) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (1242) all_67_1_96 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| From (1242) and (2337) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (928), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| From (1227) and (1933) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.07/172.29  																																																																																																																																																																																																																																																																																			| (3359) all_82_1_108 = all_18_1_20
% 223.07/172.29  																																																																																																																																																																																																																																																																																			|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| Combining equations (1249,3359) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (1227) all_18_1_20 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| Combining equations (1227,3359) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (1249) all_82_1_108 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| From (1227) and (1936) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1085), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| From (1293) and (2061) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.07/172.29  																																																																																																																																																																																																																																																																																				| (3383) all_47_2_83 = all_16_2_18
% 223.07/172.29  																																																																																																																																																																																																																																																																																				|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| Combining equations (1293,3383) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (1225) all_16_2_18 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| Combining equations (1225,3383) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| From (1293) and (2064) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1124), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| From (1227) and (1933) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.07/172.29  																																																																																																																																																																																																																																																																																					| (3375) all_18_1_20 = all_14_2_15
% 223.07/172.29  																																																																																																																																																																																																																																																																																					|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| Combining equations (1227,3375) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (1200) all_14_2_15 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| Combining equations (1200,3375) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (1227) all_18_1_20 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| From (1227) and (1936) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (889), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| From (1221) and (2081) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.07/172.29  																																																																																																																																																																																																																																																																																						| (1221) all_12_1_11 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																						|
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| From (1221) and (2084) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|
% 223.07/172.29  																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (528), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| From (1293) and (2159) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.07/172.29  																																																																																																																																																																																																																																																																																							| (3391) all_82_3_110 = all_47_2_83
% 223.07/172.29  																																																																																																																																																																																																																																																																																							|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| Combining equations (1247,3391) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (1293) all_47_2_83 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| Combining equations (1293,3391) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (1247) all_82_3_110 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| From (1293) and (2162) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (824), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| From (1282) and (2382) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.07/172.29  																																																																																																																																																																																																																																																																																								| (3413) all_24_2_30 = all_20_1_23
% 223.07/172.29  																																																																																																																																																																																																																																																																																								|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| Combining equations (1282,3413) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (1228) all_20_1_23 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| Combining equations (1228,3413) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| From (1282) and (2385) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (627), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| From (1281) and (2039) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.07/172.29  																																																																																																																																																																																																																																																																																									| (3405) all_47_3_84 = all_12_0_10
% 223.07/172.29  																																																																																																																																																																																																																																																																																									|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| Combining equations (2191,3405) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| (1281) all_12_0_10 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| Combining equations (1281,3405) yields a new equation:
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| (2191) all_47_3_84 = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| From (1281) and (2042) follows:
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|
% 223.07/172.29  																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (409), into two cases.
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.07/172.29  																																																																																																																																																																																																																																																																																										| (3425)  ~ (aNaturalNumber0(xr) = all_16_0_16)
% 223.07/172.29  																																																																																																																																																																																																																																																																																										|
% 223.07/172.29  																																																																																																																																																																																																																																																																																											| From (1292) and (3425) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| Using (88) and (8229) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																										| (3428) aNaturalNumber0(xr) = all_16_0_16
% 223.07/172.30  																																																																																																																																																																																																																																																																																										| (1292) all_16_0_16 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																										|
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| From (1292) and (3428) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| (88) aNaturalNumber0(xr) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|
% 223.07/172.30  																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (748), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| From (1282) and (2382) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.07/172.30  																																																																																																																																																																																																																																																																																											| (3421) all_47_1_82 = all_24_2_30
% 223.07/172.30  																																																																																																																																																																																																																																																																																											|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| Combining equations (1237,3421) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| Combining equations (1282,3421) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (1237) all_47_1_82 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| From (1282) and (2385) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (781), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| From (1294) and (2275) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.07/172.30  																																																																																																																																																																																																																																																																																												| (3443) all_77_2_105 = all_37_3_64
% 223.07/172.30  																																																																																																																																																																																																																																																																																												|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| Combining equations (1294,3443) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (1233) all_37_3_64 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| Combining equations (1233,3443) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (1294) all_77_2_105 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| From (1294) and (2278) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (986), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| From (1294) and (1953) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.07/172.30  																																																																																																																																																																																																																																																																																													| (3435) all_77_2_105 = all_57_1_89
% 223.07/172.30  																																																																																																																																																																																																																																																																																													|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| Combining equations (1294,3435) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (980) all_57_1_89 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| Combining equations (980,3435) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| From (1294) and (1956) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1019), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| From (1244) and (2604) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.07/172.30  																																																																																																																																																																																																																																																																																														| (3457) all_72_1_100 = all_39_8_74
% 223.07/172.30  																																																																																																																																																																																																																																																																																														|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| Combining equations (1244,3457) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (1179) all_39_8_74 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| Combining equations (1179,3457) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (1244) all_72_1_100 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| From (1244) and (2607) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (793), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (3447)  ~ (aNaturalNumber0(sz10) = all_22_1_26)
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| From (1229) and (3447) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (3450) aNaturalNumber0(sz10) = all_22_1_26
% 223.07/172.30  																																																																																																																																																																																																																																																																																															| (1229) all_22_1_26 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																															|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| From (1229) and (3450) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (512), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| (3469)  ~ (aNaturalNumber0(xk) = all_77_2_105)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| From (1294) and (3469) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| Using (1665) and (1670) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| (3472) aNaturalNumber0(xk) = all_77_2_105
% 223.07/172.30  																																																																																																																																																																																																																																																																																																| (3473) all_77_2_105 = all_52_2_87
% 223.07/172.30  																																																																																																																																																																																																																																																																																																|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| Combining equations (1294,3473) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (1674) all_52_2_87 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| Combining equations (1674,3473) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (1294) all_77_2_105 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| From (1294) and (3472) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (1665) aNaturalNumber0(xk) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (998), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| From (1233) and (3295) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	| (3465) all_57_1_89 = all_37_3_64
% 223.07/172.30  																																																																																																																																																																																																																																																																																																	|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| Combining equations (980,3465) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (1233) all_37_3_64 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| Combining equations (1233,3465) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (980) all_57_1_89 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| From (1233) and (3298) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (764), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| From (1292) and (3485) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		| (3489) all_39_7_73 = all_16_0_16
% 223.07/172.30  																																																																																																																																																																																																																																																																																																		|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| Combining equations (1236,3489) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| Combining equations (1292,3489) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (1236) all_39_7_73 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| From (1292) and (3488) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1016), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| From (1282) and (2210) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			| (3481) all_39_8_74 = all_24_2_30
% 223.07/172.30  																																																																																																																																																																																																																																																																																																			|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| Combining equations (1179,3481) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (1282) all_24_2_30 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| Combining equations (1282,3481) yields a new equation:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (1179) all_39_8_74 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| From (1282) and (2213) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (733), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| From (1237) and (2490) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				| (1237) all_47_1_82 = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																				|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| From (1237) and (2493) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1023), into two cases.
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						| From (1233) and (3295) follows:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						|
% 223.07/172.30  																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.07/172.30  																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																					| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.07/172.31  																																																																																																																																																																																																																																																																																																					| (3497) all_39_8_74 = all_37_3_64
% 223.07/172.31  																																																																																																																																																																																																																																																																																																					|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| Combining equations (1179,3497) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| (1233) all_37_3_64 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| From (1233) and (3298) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (719), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| From (1791) and (1977) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						| (3518) all_72_2_101 = all_67_1_96
% 223.07/172.31  																																																																																																																																																																																																																																																																																																						|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| Combining equations (1791,3518) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (1242) all_67_1_96 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| Combining equations (1242,3518) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (1791) all_72_2_101 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| From (1791) and (1980) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1062), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| From (1350) and (1985) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							| (3510) all_24_0_28 = all_18_2_21
% 223.07/172.31  																																																																																																																																																																																																																																																																																																							|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| Combining equations (3510,1350) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (6309) all_18_2_21 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| Simplifying 6309 yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (1226) all_18_2_21 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| From (1350) and (1988) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (427), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| From (1350) and (2136) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								| (1350) all_24_0_28 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																								|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| From (1350) and (2139) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1055), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| (3522)  ~ (aNaturalNumber0(sz10) = all_18_2_21)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| From (1226) and (3522) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| Using (61) and (1994) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| (3525) aNaturalNumber0(sz10) = all_18_2_21
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									| (1226) all_18_2_21 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																									|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| From (1226) and (3525) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| (61) aNaturalNumber0(sz10) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1130), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| (3542)  ~ (aNaturalNumber0(sz00) = all_12_2_12)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| From (1223) and (3542) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| Using (26) and (2070) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| (3545) aNaturalNumber0(sz00) = all_12_2_12
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										| (1223) all_12_2_12 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																										|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| From (1223) and (3545) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| (26) aNaturalNumber0(sz00) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1067), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| From (1244) and (2604) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											| (3538) all_72_1_100 = all_18_2_21
% 223.07/172.31  																																																																																																																																																																																																																																																																																																											|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| Combining equations (1244,3538) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (1226) all_18_2_21 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| Combining equations (1226,3538) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (1244) all_72_1_100 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| From (1244) and (2607) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (731), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| From (1674) and (3035) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												| (3560) all_67_1_96 = all_52_2_87
% 223.07/172.31  																																																																																																																																																																																																																																																																																																												|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| Combining equations (1242,3560) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (1674) all_52_2_87 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| Combining equations (1674,3560) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (1242) all_67_1_96 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| From (1674) and (3038) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1044), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| From (1242) and (2334) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													| (3552) all_67_1_96 = all_37_4_65
% 223.07/172.31  																																																																																																																																																																																																																																																																																																													|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| Combining equations (1242,3552) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (1232) all_37_4_65 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| Combining equations (1232,3552) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (1242) all_67_1_96 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| From (1242) and (2337) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (379), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (3571)  ~ (aNaturalNumber0(xr) = all_77_2_105)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| From (1294) and (3571) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| Using (88) and (8229) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (3574) aNaturalNumber0(xr) = all_77_2_105
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																														|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| From (1294) and (3574) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| (88) aNaturalNumber0(xr) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (947), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| From (1236) and (2522) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															| (3567) all_77_1_104 = all_39_7_73
% 223.07/172.31  																																																																																																																																																																																																																																																																																																															|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| Combining equations (1246,3567) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (1236) all_39_7_73 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| Combining equations (1236,3567) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (1246) all_77_1_104 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| From (1236) and (2525) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (996), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| From (1237) and (2490) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																| (3589) all_57_1_89 = all_47_1_82
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| Combining equations (980,3589) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| (1237) all_47_1_82 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| Combining equations (1237,3589) yields a new equation:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| (980) all_57_1_89 = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| From (1237) and (2493) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (945), into two cases.
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																		| From (1244) and (2604) follows:
% 223.07/172.31  																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																	| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																	| (3581) all_77_1_104 = all_72_1_100
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																	|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| Combining equations (1246,3581) yields a new equation:
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| (1244) all_72_1_100 = 0
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| Combining equations (1244,3581) yields a new equation:
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| (1246) all_77_1_104 = 0
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| From (1244) and (2607) follows:
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (624), into two cases.
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.07/172.32  																																																																																																																																																																																																																																																																																																																			| From (1350) and (2899) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																		| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																		| (3604) all_47_3_84 = all_24_0_28
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| Combining equations (2191,3604) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (1350) all_24_0_28 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| Combining equations (1350,3604) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (2191) all_47_3_84 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| From (1350) and (2902) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1052), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| From (1218) and (3165) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			| (3597) all_37_4_65 = all_14_1_14
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| Combining equations (1232,3597) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (1218) all_14_1_14 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| From (1218) and (3168) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (655), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| From (1292) and (2023) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				| (3620) all_37_2_63 = all_16_0_16
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| Combining equations (1195,3620) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (1292) all_16_0_16 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| From (1292) and (2026) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1073), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| From (1227) and (1933) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					| (3612) all_18_1_20 = all_18_2_21
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| Combining equations (1227,3612) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (1226) all_18_2_21 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| Combining equations (1226,3612) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (1227) all_18_1_20 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| From (1227) and (1936) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (625), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| From (1283) and (2007) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						| (3635) all_47_3_84 = all_26_2_33
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| Combining equations (2191,3635) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| From (1283) and (2010) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (724), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| From (1294) and (2275) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							| (3627) all_77_2_105 = all_67_1_96
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| Combining equations (1294,3627) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (1242) all_67_1_96 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| Combining equations (1242,3627) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (1294) all_77_2_105 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| From (1294) and (2278) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (792), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| From (1229) and (2891) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								| (1229) all_22_1_26 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| From (1229) and (2894) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1135), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| From (1293) and (2061) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									| (3642) all_47_2_83 = all_12_2_12
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| Combining equations (1293,3642) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (1223) all_12_2_12 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| Combining equations (1223,3642) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (1293) all_47_2_83 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| From (1293) and (2064) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1036), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| From (1293) and (2061) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										| (3664) all_47_2_83 = all_37_4_65
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| Combining equations (1293,3664) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (1232) all_37_4_65 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| Combining equations (1232,3664) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (1293) all_47_2_83 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| From (1293) and (2064) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1110), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| From (1293) and (2061) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											| (3656) all_47_2_83 = all_14_2_15
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| Combining equations (1293,3656) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (1200) all_14_2_15 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| Combining equations (1200,3656) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (1293) all_47_2_83 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| From (1293) and (2064) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1065), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| From (1281) and (2374) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												| (3680) all_18_2_21 = all_12_0_10
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| Combining equations (1226,3680) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| Combining equations (1281,3680) yields a new equation:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| (1226) all_18_2_21 = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| From (1281) and (2377) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (705), into two cases.
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														| From (1294) and (2275) follows:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.25/172.32  																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																													| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																													| (3672) all_77_2_105 = all_72_1_100
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| Combining equations (1294,3672) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| (1244) all_72_1_100 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| Combining equations (1244,3672) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| From (1294) and (2278) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (953), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| From (1218) and (3165) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														| (3694) all_77_1_104 = all_14_1_14
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| Combining equations (1246,3694) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (1218) all_14_1_14 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| Combining equations (1218,3694) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (1246) all_77_1_104 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| From (1218) and (3168) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (713), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| From (1242) and (2334) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															| (1242) all_67_1_96 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| From (1242) and (2337) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (726), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3485) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																| (3710) all_67_1_96 = all_16_0_16
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| Combining equations (1242,3710) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| Combining equations (1292,3710) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (1242) all_67_1_96 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3488) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1095), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| From (1236) and (2522) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	| (3702) all_39_7_73 = all_16_2_18
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| Combining equations (1236,3702) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (1225) all_16_2_18 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| Combining equations (1225,3702) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (1236) all_39_7_73 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| From (1236) and (2525) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (806), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| From (1350) and (2136) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		| (3725) all_24_0_28 = all_22_1_26
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| Combining equations (3725,1350) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (5268) all_22_1_26 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| Simplifying 5268 yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (1229) all_22_1_26 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| From (1350) and (2139) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1049), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| From (1228) and (2055) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			| (3718) all_37_4_65 = all_20_1_23
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| Combining equations (1232,3718) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (1228) all_20_1_23 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| From (1228) and (2058) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (772), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (3737)  ~ (aNaturalNumber0(sz00) = all_37_3_64)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| From (1233) and (3737) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| Using (26) and (2070) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (3740) aNaturalNumber0(sz00) = all_37_3_64
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				| (1233) all_37_3_64 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| From (1233) and (3740) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (672), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| From (1293) and (2159) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					| (3733) all_47_2_83 = all_26_1_32
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| Combining equations (1293,3733) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (1202) all_26_1_32 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| Combining equations (1202,3733) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (1293) all_47_2_83 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| From (1293) and (2162) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1121), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| From (1233) and (3295) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						| (3753) all_37_3_64 = all_14_2_15
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| Combining equations (1233,3753) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (1200) all_14_2_15 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| Combining equations (1200,3753) yields a new equation:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (1233) all_37_3_64 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| From (1233) and (3298) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (695), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| From (1244) and (2604) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							| (1244) all_72_1_100 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| From (1244) and (2607) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (399), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| (3763)  ~ (aNaturalNumber0(sz00) = all_47_2_83)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| From (1293) and (3763) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| Using (26) and (2070) yields:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| (3766) aNaturalNumber0(sz00) = all_47_2_83
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								| (1293) all_47_2_83 = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| From (1293) and (3766) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1104), into two cases.
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									| (3757)  ~ (aNaturalNumber0(sz10) = all_14_2_15)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																										| From (1200) and (3757) follows:
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																										| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.33  																																																																																																																																																																																																																																																																																																																																										| Using (61) and (1994) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																									| (3760) aNaturalNumber0(sz10) = all_14_2_15
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																									| (1200) all_14_2_15 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										| From (1200) and (3760) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										| (61) aNaturalNumber0(sz10) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (973), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| From (1233) and (3295) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										| (3779) all_62_1_93 = all_37_3_64
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| Combining equations (1240,3779) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (1233) all_37_3_64 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| Combining equations (1233,3779) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (1240) all_62_1_93 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| From (1233) and (3298) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (771), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (3769)  ~ (aNaturalNumber0(sz10) = all_37_3_64)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| From (1233) and (3769) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| Using (61) and (1994) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (3772) aNaturalNumber0(sz10) = all_37_3_64
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											| (1233) all_37_3_64 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| From (1233) and (3772) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| (61) aNaturalNumber0(sz10) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (459), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| (2089)  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| From (1292) and (2089) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| Using (1284) and (2090) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| (2092) aNaturalNumber0(all_0_9_9) = all_16_0_16
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												| (3795) all_26_2_33 = all_16_0_16
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| Combining equations (1283,3795) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| Combining equations (1292,3795) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (1283) all_26_2_33 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| From (1292) and (2092) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (939), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| From (1292) and (2984) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													| (3787) all_77_1_104 = all_16_0_16
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| Combining equations (1246,3787) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (1292) all_16_0_16 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| Combining equations (1292,3787) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (1246) all_77_1_104 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| From (1292) and (2987) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (430), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (3806)  ~ (aNaturalNumber0(sz00) = all_24_0_28)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| From (1350) and (3806) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| Using (26) and (2070) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (3809) aNaturalNumber0(sz00) = all_24_0_28
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														| (1350) all_24_0_28 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| From (1350) and (3809) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (640), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| From (1292) and (2023) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															| (3803) all_39_6_72 = all_16_0_16
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| Combining equations (3803,629) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (2760) all_16_0_16 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| Simplifying 2760 yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (1292) all_16_0_16 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| From (1292) and (2026) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (394), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (3819)  ~ (aNaturalNumber0(xr) = all_47_2_83)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (3819) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| Using (88) and (8229) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (3822) aNaturalNumber0(xr) = all_47_2_83
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																| (1293) all_47_2_83 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (3822) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| (88) aNaturalNumber0(xr) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (997), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| From (1236) and (2522) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	| (3816) all_57_1_89 = all_39_7_73
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| Combining equations (980,3816) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (1236) all_39_7_73 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| From (1236) and (2525) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (609), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (2007) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		| (3837) all_52_1_86 = all_26_2_33
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1238,3837) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,3837) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (1238) all_52_1_86 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (2010) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1043), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| From (1244) and (2604) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			| (3829) all_72_1_100 = all_37_4_65
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1244,3829) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| (1232) all_37_4_65 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1232,3829) yields a new equation:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| (1244) all_72_1_100 = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| From (1244) and (2607) follows:
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1102), into two cases.
% 223.25/172.34  																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																				| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| From (1221) and (2081) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																				| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																				| (3853) all_16_2_18 = all_12_1_11
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| Combining equations (3853,1225) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (3284) all_12_1_11 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| Simplifying 3284 yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (1221) all_12_1_11 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| From (1221) and (2084) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1134), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (1953) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					| (3845) all_77_2_105 = all_12_2_12
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1294,3845) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (1223) all_12_2_12 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1223,3845) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (1956) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1056), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (3865)  ~ (aNaturalNumber0(sz00) = all_18_2_21)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| From (1226) and (3865) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| Using (26) and (2070) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (3868) aNaturalNumber0(sz00) = all_18_2_21
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						| (1226) all_18_2_21 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| From (1226) and (3868) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (762), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (2275) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							| (3861) all_77_2_105 = all_39_7_73
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1294,3861) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (1236) all_39_7_73 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1236,3861) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (1294) all_77_2_105 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (2278) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (927), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| From (1228) and (2055) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								| (3883) all_82_1_108 = all_20_1_23
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1249,3883) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (1228) all_20_1_23 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1228,3883) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (1249) all_82_1_108 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| From (1228) and (2058) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (903), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (2136) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									| (3875) all_24_0_28 = all_12_1_11
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| Combining equations (3875,1350) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (3284) all_12_1_11 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| Simplifying 3284 yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (1221) all_12_1_11 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (2139) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1088), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| From (1283) and (2252) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										| (3899) all_26_2_33 = all_16_2_18
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1283,3899) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (1225) all_16_2_18 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1225,3899) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (1283) all_26_2_33 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| From (1283) and (2255) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (914), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| From (1293) and (2061) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											| (3891) all_82_1_108 = all_47_2_83
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1249,3891) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (1293) all_47_2_83 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1293,3891) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (1249) all_82_1_108 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| From (1293) and (2064) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (714), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (3911)  ~ (aNaturalNumber0(sz10) = all_67_1_96)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| From (1242) and (3911) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| Using (61) and (1994) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (3914) aNaturalNumber0(sz10) = all_67_1_96
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												| (1242) all_67_1_96 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| From (1242) and (3914) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| (61) aNaturalNumber0(sz10) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (915), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (2984) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													| (3907) all_82_1_108 = all_16_0_16
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1249,3907) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (1292) all_16_0_16 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1292,3907) yields a new equation:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (1249) all_82_1_108 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (2987) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (770), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| From (1233) and (3295) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														| (1233) all_37_3_64 = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| From (1233) and (3298) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (687), into two cases.
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																| From (1294) and (3339) follows:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.25/172.35  																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																															| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																															| (3921) all_77_2_105 = all_24_1_29
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1294,3921) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| (1207) all_24_1_29 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1207,3921) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| (1294) all_77_2_105 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| From (1294) and (3342) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (866), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| From (1281) and (1969) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																| (3943) all_16_1_17 = all_12_0_10
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (848,3943) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (1281) all_12_0_10 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| From (1281) and (1972) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (688), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2159) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	| (3935) all_47_2_83 = all_24_1_29
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1293,3935) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (1207) all_24_1_29 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1207,3935) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2162) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (373), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (3955)  ~ (aNaturalNumber0(sz00) = all_20_2_24)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (3955) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| Using (26) and (2070) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (3958) aNaturalNumber0(sz00) = all_20_2_24
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		| (1787) all_20_2_24 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (3958) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (691), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (2007) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			| (3951) all_26_2_33 = all_24_1_29
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1283,3951) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (1207) all_24_1_29 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1207,3951) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (2010) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (384), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (3969)  ~ (aNaturalNumber0(sz00) = all_77_2_105)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (3969) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| Using (26) and (2070) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (3972) aNaturalNumber0(sz00) = all_77_2_105
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				| (1294) all_77_2_105 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (3972) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (917), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| From (1283) and (2252) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					| (3965) all_82_1_108 = all_26_2_33
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1249,3965) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (1283) all_26_2_33 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1283,3965) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (1249) all_82_1_108 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| From (1283) and (2255) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (693), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (2039) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						| (3987) all_24_1_29 = all_12_0_10
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1207,3987) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (1281) all_12_0_10 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (2042) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (936), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2446) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							| (3979) all_77_1_104 = all_20_0_22
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1246,3979) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (1828) all_20_0_22 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1828,3979) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (1246) all_77_1_104 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (2449) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (729), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2382) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								| (4000) all_67_1_96 = all_24_2_30
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1242,4000) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1282,4000) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (1242) all_67_1_96 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2385) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (482), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| From (1281) and (2039) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									| (1281) all_12_0_10 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| From (1281) and (2042) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (940), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| From (1350) and (1985) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										| (4016) all_77_1_104 = all_24_0_28
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1246,4016) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1350,4016) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (1246) all_77_1_104 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| From (1350) and (1988) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (494), into two cases.
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (2312)  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2312) follows:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												| Using (1284) and (2090) yields:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (2315) aNaturalNumber0(all_0_9_9) = all_22_2_27
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											| (4008) all_22_2_27 = all_12_0_10
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (4008,1788) yields a new equation:
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												| (2959) all_12_0_10 = 0
% 223.25/172.36  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| Simplifying 2959 yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| (1281) all_12_0_10 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2315) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1020), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| From (1242) and (2334) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												| (4030) all_67_1_96 = all_39_8_74
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1242,4030) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (1179) all_39_8_74 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1179,4030) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (1242) all_67_1_96 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| From (1242) and (2337) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (751), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| From (1236) and (2522) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													| (1236) all_39_7_73 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| From (1236) and (2525) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (930), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| From (1218) and (3165) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														| (4044) all_82_1_108 = all_14_1_14
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1249,4044) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (1218) all_14_1_14 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1218,4044) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (1249) all_82_1_108 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| From (1218) and (3168) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (363), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (4034)  ~ (aNaturalNumber0(sz00) = all_22_2_27)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| From (1788) and (4034) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| Using (26) and (2070) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (4037) aNaturalNumber0(sz00) = all_22_2_27
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															| (1788) all_22_2_27 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| From (1788) and (4037) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (994), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| From (1244) and (2604) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																| (4060) all_72_1_100 = all_57_1_89
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1244,4060) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (980) all_57_1_89 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (980,4060) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (1244) all_72_1_100 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| From (1244) and (2607) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (667), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| From (1790) and (2506) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	| (4052) all_62_2_94 = all_26_1_32
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1790,4052) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (1202) all_26_1_32 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1202,4052) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (1790) all_62_2_94 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| From (1790) and (2509) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (786), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| From (1282) and (2382) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		| (4074) all_37_3_64 = all_24_2_30
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1233,4074) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (1282) all_24_2_30 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1282,4074) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (1233) all_37_3_64 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| From (1282) and (2385) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (325), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2298) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			| (1828) all_20_0_22 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2301) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (560), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2023) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				| (4090) all_72_3_102 = all_16_0_16
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1243,4090) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (1292) all_16_0_16 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2026) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1003), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| From (1218) and (3165) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					| (4082) all_57_1_89 = all_14_1_14
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (980,4082) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (1218) all_14_1_14 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1218,4082) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (980) all_57_1_89 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| From (1218) and (3168) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (674), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2899) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						| (4105) all_26_1_32 = all_24_0_28
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1202,4105) yields a new equation:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2902) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (614), into two cases.
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (2665) follows:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.25/172.37  																																																																																																																																																																																																																																																																																																																																																																																							| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																							| (4097) all_67_2_97 = all_47_3_84
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1829,4097) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| (2191) all_47_3_84 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (2191,4097) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (2668) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1137), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (1985) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								| (4120) all_24_0_28 = all_12_2_12
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (1988) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1057), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2151) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									| (4112) all_82_2_109 = all_18_2_21
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,4112) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (1226) all_18_2_21 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1226,4112) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2154) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1041), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| From (1281) and (2374) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										| (4136) all_37_4_65 = all_12_0_10
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1232,4136) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (1281) all_12_0_10 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| From (1281) and (2377) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (755), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (4124) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											| (4128) all_67_2_97 = all_39_7_73
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,4128) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (1236) all_39_7_73 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1236,4128) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (4127) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (992), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (2374) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												| (4149) all_57_1_89 = all_12_0_10
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (980,4149) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (2377) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (350), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| From (1789) and (2186) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													| (1789) all_57_2_90 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| From (1789) and (2189) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1090), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (2374) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														| (4162) all_16_2_18 = all_12_0_10
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (4162,1225) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (2959) all_12_0_10 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| Simplifying 2959 yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (2377) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1105), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (4152)  ~ (aNaturalNumber0(sz00) = all_14_2_15)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| From (1200) and (4152) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| Using (26) and (2070) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (4155) aNaturalNumber0(sz00) = all_14_2_15
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															| (1200) all_14_2_15 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| From (1200) and (4155) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (715), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| (4174)  ~ (aNaturalNumber0(sz00) = all_67_1_96)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| From (1242) and (4174) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| Using (26) and (2070) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| (4177) aNaturalNumber0(sz00) = all_67_1_96
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																| (1242) all_67_1_96 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| From (1242) and (4177) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| (26) aNaturalNumber0(sz00) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (535), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2665) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	| (4170) all_77_3_106 = all_67_2_97
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1245,4170) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,4170) yields a new equation:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (1245) all_77_3_106 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2668) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (354), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1775) and (1780) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		| (1789) all_57_2_90 = 0
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (775), into two cases.
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2298) follows:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			| (4184) all_37_3_64 = all_20_0_22
% 223.25/172.38  																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1233,4184) yields a new equation:
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| (1828) all_20_0_22 = 0
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1828,4184) yields a new equation:
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| (1233) all_37_3_64 = 0
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2301) follows:
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (410), into two cases.
% 223.25/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2023) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				| (1292) all_16_0_16 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| From (1292) and (2026) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (520), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2665) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					| (4196) all_82_3_110 = all_67_2_97
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1247,4196) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,4196) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (1247) all_82_3_110 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2668) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (381), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (2275) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (2278) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (716), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2097) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							| (4210) all_82_2_109 = all_67_1_96
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1830,4210) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (1242) all_67_1_96 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1242,4210) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2100) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (389), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (4226)  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (4226) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1295) and (2129) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (4229) aNaturalNumber0(all_0_7_7) = all_72_2_101
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								| (4230) all_77_2_105 = all_72_2_101
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1294,4230) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1791,4230) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (1294) all_77_2_105 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (4229) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (867), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| From (1674) and (3035) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									| (4224) all_52_2_87 = all_16_1_17
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1674,4224) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (848) all_16_1_17 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (848,4224) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (1674) all_52_2_87 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| From (1674) and (3038) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (440), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (4242)  ~ (aNaturalNumber0(all_0_8_8) = all_77_2_105)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (4242) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1351) and (2575) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (4245) aNaturalNumber0(all_0_8_8) = all_77_2_105
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										| (4246) all_77_2_105 = all_24_0_28
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,4246) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1350,4246) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (4245) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (856), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (1939) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											| (4238) all_62_2_94 = all_16_1_17
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1790,4238) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (848) all_16_1_17 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (848,4238) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (1790) all_62_2_94 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (1942) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (460), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (2232)  ~ (aNaturalNumber0(all_0_9_9) = all_24_0_28)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (2232) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1284) and (2090) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (2235) aNaturalNumber0(all_0_9_9) = all_24_0_28
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												| (4262) all_26_2_33 = all_24_0_28
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1283,4262) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (1350) all_24_0_28 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1350,4262) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (1283) all_26_2_33 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (2235) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (978), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| From (1218) and (3165) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													| (4254) all_62_1_93 = all_14_1_14
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1240,4254) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1218) all_14_1_14 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1218,4254) yields a new equation:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (1240) all_62_1_93 = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| From (1218) and (3168) follows:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (463), into two cases.
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.39  																																																																																																																																																																																																																																																																																																																																																																																																															| From (1282) and (2382) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																														| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																														| (1282) all_24_2_30 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| From (1282) and (2385) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (377), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2498) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1775) and (1780) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															| (4270) all_20_0_22 = all_20_2_24
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (4270,1828) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (1786) all_20_2_24 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 1786 yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (1787) all_20_2_24 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2501) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (870), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (4288)  ~ (aNaturalNumber0(sz00) = all_14_1_14)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1218) and (4288) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (26) and (2070) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (4291) aNaturalNumber0(sz00) = all_14_1_14
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																| (1218) all_14_1_14 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1218) and (4291) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| (26) aNaturalNumber0(sz00) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (984), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2120) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	| (4284) all_67_2_97 = all_57_1_89
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,4284) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (980) all_57_1_89 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (980,4284) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2123) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (974), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1229) and (2891) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		| (4306) all_62_1_93 = all_22_1_26
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1240,4306) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1229) all_22_1_26 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1229,4306) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (1240) all_62_1_93 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1229) and (2894) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1004), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1221) and (2081) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			| (4298) all_57_1_89 = all_12_1_11
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (980,4298) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (1221) all_12_1_11 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1221,4298) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (980) all_57_1_89 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1221) and (2084) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (977), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| From (848) and (2268) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				| (4320) all_62_1_93 = all_16_1_17
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1240,4320) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (848) all_16_1_17 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (848,4320) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1240) all_62_1_93 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| From (848) and (2271) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (425), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (4310)  ~ (aNaturalNumber0(xr) = all_24_0_28)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (4310) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (88) and (8229) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (4313) aNaturalNumber0(xr) = all_24_0_28
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					| (1350) all_24_0_28 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (4313) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (88) aNaturalNumber0(xr) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (585), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1791) and (2642) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						| (4334) all_72_2_101 = all_57_3_91
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1791,4334) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (2199) all_57_3_91 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (2199,4334) yields a new equation:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (1791) all_72_2_101 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1791) and (2645) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (383), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (4324)  ~ (aNaturalNumber0(sz10) = all_77_2_105)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (4324) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (61) and (1994) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (4327) aNaturalNumber0(sz10) = all_77_2_105
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (4327) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (61) aNaturalNumber0(sz10) = 0
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (616), into two cases.
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (2642) follows:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								| (4350) all_72_2_101 = all_47_3_84
% 223.43/172.40  																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1791,4350) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| (2191) all_47_3_84 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (2191,4350) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (2645) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (942), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2210) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									| (4342) all_77_1_104 = all_24_2_30
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1246,4342) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1282,4342) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1246) all_77_1_104 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2213) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (799), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (1939) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										| (4366) all_62_2_94 = all_22_1_26
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1790,4366) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1229) all_22_1_26 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1229,4366) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1790) all_62_2_94 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (1942) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (711), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1281) and (1969) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											| (4358) all_72_1_100 = all_12_0_10
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1244,4358) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1281) all_12_0_10 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1281,4358) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1244) all_72_1_100 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1281) and (1972) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (326), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2446) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2449) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (735), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| (4368)  ~ (aNaturalNumber0(sz00) = all_47_1_82)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1237) and (4368) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (26) and (2070) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| (4371) aNaturalNumber0(sz00) = all_47_1_82
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													| (1237) all_47_1_82 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1237) and (4371) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (26) aNaturalNumber0(sz00) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (634), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1790) and (2506) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														| (4392) all_62_2_94 = all_39_6_72
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1790,4392) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (629) all_39_6_72 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (629,4392) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (1790) all_62_2_94 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1790) and (2509) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1094), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1237) and (2490) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															| (4384) all_47_1_82 = all_16_2_18
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1237,4384) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (1225) all_16_2_18 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1225,4384) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (1237) all_47_1_82 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1237) and (2493) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (615), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2171) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																| (4408) all_47_3_84 = all_20_0_22
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (2191,4408) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1828) all_20_0_22 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2174) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (803), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (2275) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4400) all_77_2_105 = all_22_1_26
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1294,4400) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1229) all_22_1_26 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1229,4400) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1294) all_77_2_105 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1294) and (2278) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (802), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2366) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4423) all_22_1_26 = all_20_2_24
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (4423,1229) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1786) all_20_2_24 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| Simplifying 1786 yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2369) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1042), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (2552) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4415) all_52_2_87 = all_37_4_65
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1674,4415) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1232) all_37_4_65 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1232,4415) yields a new equation:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1674) all_52_2_87 = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (2555) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (610), into two cases.
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1282) and (2475) follows:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.41  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4436) all_52_1_86 = all_24_2_30
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1238,4436) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1282) all_24_2_30 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1282,4436) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1238) all_52_1_86 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1282) and (2478) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (382), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (1953) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (1956) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (956), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4448)  ~ (aNaturalNumber0(sz10) = all_62_1_93)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1240) and (4448) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (61) and (1994) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4451) aNaturalNumber0(sz10) = all_62_1_93
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1240) all_62_1_93 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1240) and (4451) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (61) aNaturalNumber0(sz10) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1144), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1237) and (2490) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4444) all_47_1_82 = all_12_2_12
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1237,4444) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1223) all_12_2_12 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1223,4444) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1237) all_47_1_82 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1237) and (2493) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (456), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2218)  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1787) and (2218) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1284) and (2090) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2221) aNaturalNumber0(all_0_9_9) = all_20_2_24
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4466) all_26_2_33 = all_20_2_24
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1283,4466) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1787) all_20_2_24 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1787,4466) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1283) all_26_2_33 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1787) and (2221) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1071), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1233) and (3295) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4458) all_37_3_64 = all_18_2_21
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1233,4458) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1226) all_18_2_21 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1226,4458) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1233) all_37_3_64 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1233) and (3298) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (315), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4478)  ~ (aNaturalNumber0(xr) = all_67_2_97)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4478) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (88) and (8229) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4481) aNaturalNumber0(xr) = all_67_2_97
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1829) all_67_2_97 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4481) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (88) aNaturalNumber0(xr) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (745), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1293) and (2962) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4474) all_47_1_82 = all_47_2_83
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1237,4474) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1293) all_47_2_83 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1293,4474) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1237) all_47_1_82 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1293) and (2965) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (372), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4492)  ~ (aNaturalNumber0(sz10) = all_20_2_24)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (4492) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (61) and (1994) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4495) aNaturalNumber0(sz10) = all_20_2_24
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1787) all_20_2_24 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (4495) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (61) aNaturalNumber0(sz10) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1014), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (1985) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4488) all_39_8_74 = all_24_0_28
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1179,4488) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1350) all_24_0_28 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1350,4488) yields a new equation:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1179) all_39_8_74 = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (1988) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (507), into two cases.
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4502)  ~ (aNaturalNumber0(xk) = all_72_2_101)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1791) and (4502) follows:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1665) and (1670) yields:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4505) aNaturalNumber0(xk) = all_72_2_101
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4506) all_72_2_101 = all_52_2_87
% 223.43/172.42  																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1791,4506) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1674) all_52_2_87 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1674,4506) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1791) all_72_2_101 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1791) and (4505) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1665) aNaturalNumber0(xk) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (364), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1775) and (1780) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1788) all_22_2_27 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (868), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1218) and (3165) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1218) all_14_1_14 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1218) and (3168) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (854), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2298) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4514) all_20_0_22 = all_16_1_17
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (4514,1828) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4239) all_16_1_17 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Simplifying 4239 yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (848) all_16_1_17 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2301) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (747), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (3028) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4536) all_47_1_82 = all_26_2_33
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1237,4536) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,4536) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1237) all_47_1_82 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (3031) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (680), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1829) and (2665) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4528) all_67_2_97 = all_24_1_29
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1829,4528) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1207) all_24_1_29 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1207,4528) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1829) all_67_2_97 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1829) and (2668) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (402), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4548)  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (4548) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1295) and (2129) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4551) aNaturalNumber0(all_0_7_7) = all_67_2_97
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4552) all_67_2_97 = all_47_2_83
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,4552) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1293,4552) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (4551) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (835), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1790) and (1939) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4544) all_62_2_94 = all_18_1_20
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1790,4544) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1227) all_18_1_20 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1227,4544) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1790) all_62_2_94 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1790) and (1942) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (536), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2171) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4568) all_77_3_106 = all_20_0_22
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1245,4568) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1828) all_20_0_22 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1828,4568) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1245) all_77_3_106 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2174) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (663), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2112) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4560) all_82_2_109 = all_26_1_32
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1830,4560) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1202) all_26_1_32 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1202,4560) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2115) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (982), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4580)  ~ (aNaturalNumber0(sz00) = all_57_1_89)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (980) and (4580) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (26) and (2070) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4583) aNaturalNumber0(sz00) = all_57_1_89
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (980) all_57_1_89 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (980) and (4583) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (26) aNaturalNumber0(sz00) = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1131), into two cases.
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2151) follows:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4576) all_82_2_109 = all_12_2_12
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,4576) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1223) all_12_2_12 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1223,4576) yields a new equation:
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.43  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2154) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1084), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (1953) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4596) all_77_2_105 = all_16_2_18
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1294,4596) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1225) all_16_2_18 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1225,4596) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1294) all_77_2_105 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1294) and (1956) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (370), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2031) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1787) all_20_2_24 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2034) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1001), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1227) and (1933) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4612) all_57_1_89 = all_18_1_20
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (980,4612) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1227) all_18_1_20 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1227,4612) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (980) all_57_1_89 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1227) and (1936) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (758), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1790) and (1939) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4604) all_62_2_94 = all_39_7_73
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1790,4604) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1236) all_39_7_73 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1236,4604) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1790) all_62_2_94 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1790) and (1942) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (787), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (1969) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4628) all_37_3_64 = all_12_0_10
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1233,4628) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (1972) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (568), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2171) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4620) all_67_3_98 = all_20_0_22
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1241,4620) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1828) all_20_0_22 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1828,4620) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1241) all_67_3_98 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2174) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (698), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (4124) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4643) all_72_1_100 = all_67_2_97
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1244,4643) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,4643) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1244) all_72_1_100 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (4127) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1132), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2120) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4635) all_67_2_97 = all_12_2_12
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,4635) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1223) all_12_2_12 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1223,4635) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2123) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (912), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2446) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4659) all_82_1_108 = all_20_0_22
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1249,4659) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1828) all_20_0_22 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1828,4659) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1249) all_82_1_108 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2449) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (807), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (3028) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4651) all_26_2_33 = all_22_1_26
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1283,4651) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1229) all_22_1_26 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1229,4651) yields a new equation:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (3031) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (543), into two cases.
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2159) follows:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4674) all_77_3_106 = all_47_2_83
% 223.43/172.44  																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1245,4674) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2162) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (670), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1787) and (2031) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4667) all_26_1_32 = all_20_2_24
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1202,4667) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1787) all_20_2_24 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1787) and (2034) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (466), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4685)  ~ (aNaturalNumber0(sz00) = all_24_2_30)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1282) and (4685) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (26) and (2070) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4688) aNaturalNumber0(sz00) = all_24_2_30
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1282) all_24_2_30 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1282) and (4688) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (26) aNaturalNumber0(sz00) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (777), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1790) and (1939) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4681) all_62_2_94 = all_37_3_64
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1790,4681) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1233) all_37_3_64 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1233,4681) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1790) all_62_2_94 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1790) and (1942) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (706), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1293) and (2962) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4703) all_72_1_100 = all_47_2_83
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1244,4703) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1293) all_47_2_83 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1293,4703) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1244) all_72_1_100 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1293) and (2965) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (898), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2144) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4695) all_22_2_27 = all_12_1_11
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (4695,1788) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3284) all_12_1_11 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Simplifying 3284 yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1221) all_12_1_11 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2147) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (525), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2105) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4718) all_82_3_110 = all_22_2_27
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1247,4718) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1788,4718) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1247) all_82_3_110 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2108) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1026), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1227) and (1933) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4711) all_39_8_74 = all_18_1_20
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1179,4711) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1227) all_18_1_20 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1227) and (1936) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (553), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (2642) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4734) all_72_2_101 = all_72_3_102
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1791,4734) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1243) all_72_3_102 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1243,4734) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (2645) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1070), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1236) and (2522) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4726) all_39_7_73 = all_18_2_21
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1236,4726) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1226) all_18_2_21 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1226,4726) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1236) all_39_7_73 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1236) and (2525) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (738), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2298) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4750) all_47_1_82 = all_20_0_22
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1237,4750) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2301) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (679), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2112) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4742) all_82_2_109 = all_24_1_29
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1830,4742) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1207) all_24_1_29 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1207,4742) yields a new equation:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2115) follows:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (951), into two cases.
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.45  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1227) and (1933) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4763) all_77_1_104 = all_18_1_20
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1246,4763) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1227) all_18_1_20 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1227,4763) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1246) all_77_1_104 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1227) and (1936) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (586), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1790) and (2506) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4757) all_62_2_94 = all_57_3_91
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1790,4757) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2199) all_57_3_91 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (2199,4757) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1790) all_62_2_94 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1790) and (2509) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (637), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2031) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4779) all_39_6_72 = all_20_2_24
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (4779,629) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1786) all_20_2_24 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Simplifying 1786 yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2034) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (833), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2298) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4771) all_20_0_22 = all_18_1_20
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (4771,1828) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4545) all_18_1_20 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Simplifying 4545 yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1227) all_18_1_20 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1828) and (2301) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1000), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1228) and (2055) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4794) all_57_1_89 = all_20_1_23
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (980,4794) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1228) all_20_1_23 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1228) and (2058) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (911), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2120) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4786) all_82_1_108 = all_67_2_97
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1249,4786) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,4786) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1249) all_82_1_108 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2123) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (635), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1789) and (2186) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4809) all_57_2_90 = all_39_6_72
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1789,4809) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (629) all_39_6_72 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (629,4809) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1789) all_57_2_90 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1789) and (2189) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (542), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (3339) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4801) all_77_2_105 = all_77_3_106
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1294,4801) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1245) all_77_3_106 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1245,4801) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1294) all_77_2_105 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1294) and (3342) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (492), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4821)  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1790) and (4821) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1284) and (2090) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4824) aNaturalNumber0(all_0_9_9) = all_62_2_94
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4825) all_62_2_94 = all_12_0_10
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1790,4825) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1281) all_12_0_10 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1281,4825) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1790) all_62_2_94 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1790) and (4824) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (728), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1283) and (3028) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4817) all_67_1_96 = all_26_2_33
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1242,4817) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1283) all_26_2_33 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1283,4817) yields a new equation:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1242) all_67_1_96 = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1283) and (3031) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1059), into two cases.
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2446) follows:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4841) all_20_0_22 = all_18_2_21
% 223.43/172.46  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (4841,1828) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6309) all_18_2_21 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Simplifying 6309 yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1226) all_18_2_21 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2449) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1089), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2210) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4833) all_24_2_30 = all_16_2_18
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1282,4833) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1225) all_16_2_18 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1225,4833) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2213) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (685), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1788) and (2105) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4857) all_24_1_29 = all_22_2_27
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1207,4857) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1788) all_22_2_27 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1788) and (2108) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (995), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (2334) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4849) all_67_1_96 = all_57_1_89
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1242,4849) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (980) all_57_1_89 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (980,4849) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1242) all_67_1_96 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (2337) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (701), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1790) and (1939) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4872) all_72_1_100 = all_62_2_94
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1244,4872) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1790) all_62_2_94 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1790,4872) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1244) all_72_1_100 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1790) and (1942) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (931), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1221) and (2081) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4864) all_82_1_108 = all_12_1_11
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1249,4864) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1221) all_12_1_11 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1221,4864) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1249) all_82_1_108 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1221) and (2084) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (723), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1787) and (2366) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4888) all_67_1_96 = all_20_2_24
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1242,4888) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1787) all_20_2_24 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1787,4888) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1242) all_67_1_96 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1787) and (2369) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1061), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1292) and (2984) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (4880) all_18_2_21 = all_16_0_16
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1226,4880) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1292,4880) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1226) all_18_2_21 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1292) and (2987) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (397), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2061) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2064) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1051), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (848) and (2268) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (4896) all_37_4_65 = all_16_1_17
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1232,4896) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (848) all_16_1_17 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (848,4896) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1232) all_37_4_65 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (848) and (2271) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (737), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (4124) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4918) all_67_2_97 = all_47_1_82
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,4918) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1237) all_47_1_82 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1237,4918) yields a new equation:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (4127) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (671), into two cases.
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (3339) follows:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.43/172.47  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (4910) all_77_2_105 = all_26_1_32
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1294,4910) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1202) all_26_1_32 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1202,4910) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (3342) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (561), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2899) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4934) all_72_3_102 = all_24_0_28
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1243,4934) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1350,4934) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1243) all_72_3_102 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2902) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (967), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1281) and (2374) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4926) all_62_1_93 = all_12_0_10
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1240,4926) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1281) all_12_0_10 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1281,4926) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1240) all_62_1_93 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1281) and (2377) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (664), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1829) and (2665) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (4948) all_67_2_97 = all_26_1_32
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1829,4948) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1202) all_26_1_32 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1202,4948) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1829) all_67_2_97 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1829) and (2668) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (909), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4938)  ~ (aNaturalNumber0(sz00) = all_82_1_108)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1249) and (4938) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (26) and (2070) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4941) aNaturalNumber0(sz00) = all_82_1_108
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1249) all_82_1_108 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1249) and (4941) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (26) aNaturalNumber0(sz00) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (357), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2498) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1775) and (1780) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4964) all_57_2_90 = all_20_0_22
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1789,4964) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1828) all_20_0_22 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1828,4964) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1789) all_57_2_90 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2501) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (913), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (1953) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4956) all_82_1_108 = all_77_2_105
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1249,4956) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1294) all_77_2_105 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1294,4956) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1249) all_82_1_108 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (1956) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (522), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (2642) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4980) all_82_3_110 = all_72_2_101
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1247,4980) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (2645) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (921), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1244) and (2604) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4972) all_82_1_108 = all_72_1_100
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1249,4972) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1244) all_72_1_100 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1244,4972) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1249) all_82_1_108 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1244) and (2607) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (926), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1229) and (2891) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4995) all_82_1_108 = all_22_1_26
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1249,4995) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1229) all_22_1_26 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1229,4995) yields a new equation:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1249) all_82_1_108 = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1229) and (2894) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (690), into two cases.
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2899) follows:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (4987) all_24_0_28 = all_24_1_29
% 223.43/172.48  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (4987,1350) yields a new equation:
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5308) all_24_1_29 = 0
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 5308 yields:
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1207) all_24_1_29 = 0
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2902) follows:
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (433), into two cases.
% 223.43/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5006)  ~ (aNaturalNumber0(all_0_8_8) = all_67_2_97)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (5006) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1351) and (2575) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5009) aNaturalNumber0(all_0_8_8) = all_67_2_97
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5010) all_67_2_97 = all_24_0_28
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,5010) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1350) all_24_0_28 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1350,5010) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (5009) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (689), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1292) and (2023) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5003) all_24_1_29 = all_16_0_16
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1207,5003) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1292) and (2026) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (406), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5022)  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (5022) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1295) and (2129) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5025) aNaturalNumber0(all_0_7_7) = all_57_2_90
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5026) all_57_2_90 = all_47_2_83
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1789,5026) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1293,5026) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1789) all_57_2_90 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (5025) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (916), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1350) and (1985) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5018) all_82_1_108 = all_24_0_28
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1249,5018) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1350) all_24_0_28 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1350,5018) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1249) all_82_1_108 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1350) and (1988) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (613), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1830) and (2112) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5042) all_82_2_109 = all_47_3_84
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1830,5042) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2191) all_47_3_84 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (2191,5042) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1830) all_82_2_109 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1830) and (2115) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (918), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2210) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5034) all_82_1_108 = all_24_2_30
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1249,5034) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1282) all_24_2_30 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1282,5034) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1249) all_82_1_108 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2213) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (642), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1283) and (2007) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5058) all_39_6_72 = all_26_2_33
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (5058,629) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (11061) all_26_2_33 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Simplifying 11061 yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1283) and (2010) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (438), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5046)  ~ (aNaturalNumber0(all_0_8_8) = all_22_2_27)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1788) and (5046) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1351) and (2575) yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5049) aNaturalNumber0(all_0_8_8) = all_22_2_27
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5050) all_24_0_28 = all_22_2_27
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (5050,1350) yields a new equation:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5091) all_22_2_27 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Simplifying 5091 yields:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1788) all_22_2_27 = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1788) and (5049) follows:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (985), into two cases.
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.49  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1828) and (2446) follows:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5074) all_57_1_89 = all_20_0_22
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (980,5074) yields a new equation:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1828) all_20_0_22 = 0
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1828,5074) yields a new equation:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (980) all_57_1_89 = 0
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1828) and (2449) follows:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (877), into two cases.
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2144) follows:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5066) all_22_2_27 = all_14_1_14
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (5066,1788) yields a new equation:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1217) all_14_1_14 = 0
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Simplifying 1217 yields:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1218) all_14_1_14 = 0
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2147) follows:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (510), into two cases.
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5086)  ~ (aNaturalNumber0(xk) = all_22_2_27)
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (5086) follows:
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.61/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1665) and (1670) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5089) aNaturalNumber0(xk) = all_22_2_27
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5090) all_52_2_87 = all_22_2_27
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1674,5090) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1788,5090) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1674) all_52_2_87 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (5089) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1665) aNaturalNumber0(xk) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (590), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (3339) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5082) all_77_2_105 = all_57_3_91
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1294,5082) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2199) all_57_3_91 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (2199,5082) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1294) all_77_2_105 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (3342) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1096), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1233) and (3295) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5106) all_37_3_64 = all_16_2_18
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1233,5106) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1225) all_16_2_18 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1225,5106) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1233) all_37_3_64 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1233) and (3298) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (517), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5094)  ~ (aNaturalNumber0(xk) = all_24_2_30)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1282) and (5094) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1665) and (1670) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5097) aNaturalNumber0(xk) = all_24_2_30
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5098) all_52_2_87 = all_24_2_30
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1674,5098) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1282) all_24_2_30 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1282,5098) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1674) all_52_2_87 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1282) and (5097) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1665) aNaturalNumber0(xk) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (312), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5118)  ~ (aNaturalNumber0(sz10) = all_82_2_109)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (5118) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5121) aNaturalNumber0(sz10) = all_82_2_109
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1830) all_82_2_109 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (5121) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (519), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2112) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5114) all_82_2_109 = all_82_3_110
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1830,5114) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1247) all_82_3_110 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1247,5114) yields a new equation:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (2115) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (445), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1283) and (2252) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1283) all_26_2_33 = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1283) and (2255) follows:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (465), into two cases.
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5124)  ~ (aNaturalNumber0(sz10) = all_24_2_30)
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.50  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1282) and (5124) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (61) and (1994) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5127) aNaturalNumber0(sz10) = all_24_2_30
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1282) all_24_2_30 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1282) and (5127) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (61) aNaturalNumber0(sz10) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (636), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1788) and (2105) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5148) all_39_6_72 = all_22_2_27
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (5148,629) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5091) all_22_2_27 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Simplifying 5091 yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1788) all_22_2_27 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1788) and (2108) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (595), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1282) and (2475) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5140) all_57_3_91 = all_24_2_30
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (2199,5140) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1282) all_24_2_30 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1282,5140) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2199) all_57_3_91 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1282) and (2478) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (675), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1283) and (2007) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5162) all_26_1_32 = all_26_2_33
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1202,5162) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1283) all_26_2_33 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1283) and (2010) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1050), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1227) and (1933) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5155) all_37_4_65 = all_18_1_20
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1232,5155) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1227) all_18_1_20 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1227) and (1936) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (352), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5173)  ~ (aNaturalNumber0(sz10) = all_57_2_90)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1789) and (5173) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (61) and (1994) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5176) aNaturalNumber0(sz10) = all_57_2_90
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1789) all_57_2_90 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1789) and (5176) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (61) aNaturalNumber0(sz10) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (506), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5165)  ~ (aNaturalNumber0(xk) = all_20_0_22)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (5165) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1665) and (1670) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5168) aNaturalNumber0(xk) = all_20_0_22
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5169) all_52_2_87 = all_20_0_22
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1674,5169) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1828) all_20_0_22 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1828,5169) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1674) all_52_2_87 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1828) and (5168) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1665) aNaturalNumber0(xk) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (524), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (2186) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5191) all_82_3_110 = all_57_2_90
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1247,5191) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1789) all_57_2_90 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1789,5191) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1247) all_82_3_110 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (2189) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (760), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2144) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5183) all_39_7_73 = all_22_2_27
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1236,5183) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1788) all_22_2_27 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1788,5183) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1236) all_39_7_73 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1788) and (2147) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1075), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1218) and (3165) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5207) all_18_2_21 = all_14_1_14
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1226,5207) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1218) all_14_1_14 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1218) and (3168) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (798), into two cases.
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1791) and (1977) follows:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5199) all_72_2_101 = all_22_1_26
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1791,5199) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1229) all_22_1_26 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1229,5199) yields a new equation:
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1791) all_72_2_101 = 0
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.51  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1791) and (1980) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (471), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5216)  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (5216) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1284) and (2090) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5219) aNaturalNumber0(all_0_9_9) = all_72_2_101
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5220) all_72_2_101 = all_24_2_30
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1791,5220) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1282,5220) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (5219) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (649), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1790) and (2506) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5214) all_62_2_94 = all_37_2_63
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1790,5214) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1195) all_37_2_63 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1195,5214) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1790) all_62_2_94 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1790) and (2509) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (761), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1787) and (2366) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5236) all_39_7_73 = all_20_2_24
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1236,5236) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1787) all_20_2_24 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1787) and (2369) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (865), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1282) and (2382) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5228) all_24_2_30 = all_16_1_17
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1282,5228) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (848) all_16_1_17 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (848,5228) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1282) all_24_2_30 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1282) and (2385) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (742), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1788) and (2144) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5251) all_47_1_82 = all_22_2_27
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1237,5251) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1788) all_22_2_27 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1788,5251) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1237) all_47_1_82 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1788) and (2147) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (645), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (2112) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5243) all_82_2_109 = all_37_2_63
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1830,5243) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1195) all_37_2_63 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1195,5243) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1830) all_82_2_109 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (2115) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (809), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (3035) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5267) all_52_2_87 = all_22_1_26
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1674,5267) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1229) all_22_1_26 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1229,5267) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1674) all_52_2_87 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (3038) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (573), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2031) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5259) all_67_3_98 = all_20_2_24
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1241,5259) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1787) all_20_2_24 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1787,5259) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1241) all_67_3_98 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2034) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1122), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1229) and (2891) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5283) all_22_1_26 = all_14_2_15
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1229) and (2894) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (666), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1791) and (2642) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5275) all_72_2_101 = all_26_1_32
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1791,5275) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1202) all_26_1_32 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1202,5275) yields a new equation:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1791) all_72_2_101 = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1791) and (2645) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (834), into two cases.
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1791) and (1977) follows:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.62/172.52  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5299) all_72_2_101 = all_18_1_20
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1791,5299) yields a new equation:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1227) all_18_1_20 = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1227,5299) yields a new equation:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1791) all_72_2_101 = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1791) and (1980) follows:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1008), into two cases.
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2151) follows:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5291) all_82_2_109 = all_39_8_74
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1830,5291) yields a new equation:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1179) all_39_8_74 = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1179,5291) yields a new equation:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2154) follows:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (795), into two cases.
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2097) follows:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5315) all_82_2_109 = all_22_1_26
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1830,5315) yields a new equation:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1229) all_22_1_26 = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1229,5315) yields a new equation:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2100) follows:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (683), into two cases.
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1790) and (2506) follows:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.62/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5307) all_62_2_94 = all_24_1_29
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1790,5307) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1207) all_24_1_29 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1207,5307) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1790) all_62_2_94 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1790) and (2509) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (657), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2007)  ~ (aNaturalNumber0(xp) = all_26_2_33)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1283) and (2007) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2010) aNaturalNumber0(xp) = all_26_2_33
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5331) all_37_2_63 = all_26_2_33
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1195,5331) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1283) all_26_2_33 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1283,5331) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1195) all_37_2_63 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1283) and (2010) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1082), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (2120) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5323) all_67_2_97 = all_16_2_18
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,5323) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1225) all_16_2_18 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1225,5323) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (2123) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (784), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (2136) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5347) all_37_3_64 = all_24_0_28
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1233,5347) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1350) all_24_0_28 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1350,5347) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1233) all_37_3_64 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1350) and (2139) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (386), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3255)  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (3255) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1295) and (2129) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3258) aNaturalNumber0(all_0_7_7) = all_82_2_109
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5339) all_82_2_109 = all_77_2_105
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1830,5339) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1294,5339) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1830) all_82_2_109 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (3258) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (656), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2899) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5363) all_37_2_63 = all_24_0_28
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1195,5363) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1350) all_24_0_28 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2902) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (584), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2171) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5355) all_57_3_91 = all_20_0_22
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (2199,5355) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1828) all_20_0_22 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1828,5355) yields a new equation:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2199) all_57_3_91 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1828) and (2174) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (317), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (4124) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1829) all_67_2_97 = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (4127) follows:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (415), into two cases.
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1295) and (2129) yields:
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.65/172.53  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1032), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (2151) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5386) all_82_2_109 = all_37_4_65
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1830,5386) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1232) all_37_4_65 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1232,5386) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1830) all_82_2_109 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (2154) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (486), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5376)  ~ (aNaturalNumber0(sz00) = all_12_0_10)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1281) and (5376) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (26) and (2070) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5379) aNaturalNumber0(sz00) = all_12_0_10
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1281) all_12_0_10 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1281) and (5379) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (26) aNaturalNumber0(sz00) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1048), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1229) and (2891) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5400) all_37_4_65 = all_22_1_26
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1232,5400) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1229) all_22_1_26 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1229) and (2894) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (484), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1281) and (2374) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1281) all_12_0_10 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1281) and (2377) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1045), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1237) and (2490) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5415) all_47_1_82 = all_37_4_65
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1237,5415) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1232) all_37_4_65 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1232,5415) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1237) all_47_1_82 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1237) and (2493) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (497), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2467)  ~ (aNaturalNumber0(all_0_9_9) = all_47_2_83)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1293) and (2467) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1284) and (2090) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2470) aNaturalNumber0(all_0_9_9) = all_47_2_83
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5407) all_47_2_83 = all_12_0_10
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1293,5407) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1281) all_12_0_10 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1281,5407) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1293) all_47_2_83 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1293) and (2470) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (843), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1283) and (3028) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5430) all_26_2_33 = all_18_1_20
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1283,5430) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1227) all_18_1_20 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1227,5430) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1283) all_26_2_33 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1283) and (3031) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (478), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2089)  ~ (aNaturalNumber0(all_0_9_9) = all_16_0_16)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1292) and (2089) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1284) and (2090) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2092) aNaturalNumber0(all_0_9_9) = all_16_0_16
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5423) all_24_2_30 = all_16_0_16
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1282,5423) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1292) all_16_0_16 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1292) and (2092) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (422), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2620)  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2620) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1295) and (2129) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2623) aNaturalNumber0(all_0_7_7) = all_22_2_27
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5446) all_22_2_27 = all_16_0_16
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (5446,1788) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2760) all_16_0_16 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Simplifying 2760 yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1292) all_16_0_16 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2623) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (476), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2326)  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (2326) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1284) and (2090) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2329) aNaturalNumber0(all_0_9_9) = all_77_2_105
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5438) all_77_2_105 = all_24_2_30
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1294,5438) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1282,5438) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1294) all_77_2_105 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (2329) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (709), into two cases.
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (3028) follows:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5461) all_72_1_100 = all_26_2_33
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1244,5461) yields a new equation:
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1283) all_26_2_33 = 0
% 223.65/172.54  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1283,5461) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1244) all_72_1_100 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (3031) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (577), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (2899) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (9) and (2008) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5454) all_67_3_98 = all_24_0_28
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1241,5454) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1350) all_24_0_28 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1350) and (2902) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (9) aNaturalNumber0(xp) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (744), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1294) and (2275) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5476) all_77_2_105 = all_47_1_82
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1294,5476) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1237) all_47_1_82 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1237,5476) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1294) all_77_2_105 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1294) and (2278) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (346), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (5464) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1775) and (1780) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5468) all_82_2_109 = all_62_2_94
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1830,5468) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1790) all_62_2_94 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1790,5468) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (5467) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1101), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1218) and (3165) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5492) all_16_2_18 = all_14_1_14
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (5492,1225) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1217) all_14_1_14 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Simplifying 1217 yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1218) all_14_1_14 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1218) and (3168) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (338), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (5480) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1775) and (1780) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5484) all_72_2_101 = all_67_2_97
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1791,5484) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,5484) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1791) all_72_2_101 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (5483) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1141), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (2552) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5506) all_52_2_87 = all_12_2_12
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1674,5506) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1223) all_12_2_12 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1223,5506) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1674) all_52_2_87 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (2555) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (343), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5496)  ~ (aNaturalNumber0(sz10) = all_62_2_94)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1790) and (5496) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (61) and (1994) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5499) aNaturalNumber0(sz10) = all_62_2_94
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1790) all_62_2_94 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1790) and (5499) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (61) aNaturalNumber0(sz10) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1119), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1237) and (2490) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2493) aNaturalNumber0(xn) = all_47_1_82
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5520) all_47_1_82 = all_14_2_15
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1237,5520) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1200) all_14_2_15 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1200,5520) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1237) all_47_1_82 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1237) and (2493) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (532), into two cases.
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2475) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5512) all_82_3_110 = all_24_2_30
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1247,5512) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1282) all_24_2_30 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1282,5512) yields a new equation:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1247) all_82_3_110 = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2478) follows:
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.65/172.55  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (650), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1789) and (2186) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5536) all_57_2_90 = all_37_2_63
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1789,5536) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1195) all_37_2_63 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1195,5536) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1789) all_57_2_90 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1789) and (2189) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (530), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (2899) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5528) all_82_3_110 = all_24_0_28
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1247,5528) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1350) all_24_0_28 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1350,5528) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1247) all_82_3_110 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (2902) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (754), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2097) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5552) all_82_2_109 = all_39_7_73
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1830,5552) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1236) all_39_7_73 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1236,5552) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2100) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (547), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2475) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5544) all_77_3_106 = all_24_2_30
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1245,5544) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1282,5544) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1245) all_77_3_106 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2478) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (375), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (5464) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1775) and (1780) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5568) all_82_2_109 = all_20_2_24
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1830,5568) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1787) all_20_2_24 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1787,5568) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1830) all_82_2_109 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (5467) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (545), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1350) and (2899) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5560) all_77_3_106 = all_24_0_28
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1245,5560) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1350) all_24_0_28 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1350,5560) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1245) all_77_3_106 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1350) and (2902) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (511), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5580)  ~ (aNaturalNumber0(xk) = all_20_2_24)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (5580) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1665) and (1670) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5583) aNaturalNumber0(xk) = all_20_2_24
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5584) all_52_2_87 = all_20_2_24
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1674,5584) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1787) all_20_2_24 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1787,5584) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1674) all_52_2_87 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (5583) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1665) aNaturalNumber0(xk) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (862), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (3485) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5576) all_16_0_16 = all_16_1_17
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1292,5576) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (848) all_16_1_17 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (848,5576) yields a new equation:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1292) all_16_0_16 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (3488) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (327), into two cases.
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5594)  ~ (aNaturalNumber0(sz10) = all_20_0_22)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (5594) follows:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5597) aNaturalNumber0(sz10) = all_20_0_22
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1828) all_20_0_22 = 0
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.56  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (5597) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (850), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5588)  ~ (aNaturalNumber0(sz10) = all_16_1_17)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (848) and (5588) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5591) aNaturalNumber0(sz10) = all_16_1_17
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (848) all_16_1_17 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (848) and (5591) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (987), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2061) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5612) all_57_1_89 = all_47_2_83
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (980,5612) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1293) all_47_2_83 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1293,5612) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (980) all_57_1_89 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1293) and (2064) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1147), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1229) and (2891) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5604) all_22_1_26 = all_12_2_12
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1229) and (2894) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (763), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2962) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5628) all_47_2_83 = all_39_7_73
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1293,5628) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1236) all_39_7_73 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1236,5628) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2965) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (391), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5022)  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1789) and (5022) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1295) and (2129) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5025) aNaturalNumber0(all_0_7_7) = all_57_2_90
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5620) all_77_2_105 = all_57_2_90
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1294,5620) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1789) all_57_2_90 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1789,5620) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1294) all_77_2_105 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1789) and (5025) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (631), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2665) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5644) all_67_2_97 = all_39_6_72
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,5644) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (629) all_39_6_72 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (629,5644) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (2668) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (376), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (5480) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1775) and (1780) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5636) all_67_2_97 = all_20_2_24
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,5636) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1787) all_20_2_24 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1787,5636) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (5483) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1047), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1233) and (3295) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5660) all_37_3_64 = all_37_4_65
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1233,5660) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1232) all_37_4_65 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1232,5660) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1233) all_37_3_64 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1233) and (3298) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (717), into two cases.
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (4124) follows:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5652) all_67_1_96 = all_67_2_97
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1242,5652) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1829,5652) yields a new equation:
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1242) all_67_1_96 = 0
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.57  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (4127) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (310), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2097) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2100) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (452), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5216)  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (5216) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1284) and (2090) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5219) aNaturalNumber0(all_0_9_9) = all_72_2_101
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5668) all_72_2_101 = all_26_2_33
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1791,5668) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1283) all_26_2_33 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1283,5668) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (5219) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1118), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1242) and (2334) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5690) all_67_1_96 = all_14_2_15
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1242,5690) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1200) all_14_2_15 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1200,5690) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1242) all_67_1_96 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1242) and (2337) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (468), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2290)  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1830) and (2290) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1284) and (2090) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2293) aNaturalNumber0(all_0_9_9) = all_82_2_109
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5682) all_82_2_109 = all_24_2_30
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1830,5682) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1282,5682) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1830) all_82_2_109 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1830) and (2293) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (533), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (2039) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5706) all_82_3_110 = all_12_0_10
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1247,5706) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1281,5706) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1247) all_82_3_110 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (2042) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (472), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4821)  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1790) and (4821) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1284) and (2090) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (4824) aNaturalNumber0(all_0_9_9) = all_62_2_94
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5698) all_62_2_94 = all_24_2_30
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1790,5698) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1282) all_24_2_30 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1282,5698) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1790) all_62_2_94 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1790) and (4824) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (485), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5718)  ~ (aNaturalNumber0(sz10) = all_12_0_10)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (5718) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5721) aNaturalNumber0(sz10) = all_12_0_10
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (5721) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (515), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5710)  ~ (aNaturalNumber0(xk) = all_24_0_28)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (5710) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1665) and (1670) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5713) aNaturalNumber0(xk) = all_24_0_28
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5714) all_52_2_87 = all_24_0_28
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1674,5714) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1350) all_24_0_28 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1350,5714) yields a new equation:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1674) all_52_2_87 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (5713) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1665) aNaturalNumber0(xk) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (873), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2298) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5732) all_20_0_22 = all_14_1_14
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2301) follows:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (448), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1284) and (2090) yields:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1283) all_26_2_33 = 0
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (371), into two cases.
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.58  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2366) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1787) all_20_2_24 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2369) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (398), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5736)  ~ (aNaturalNumber0(sz10) = all_47_2_83)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (5736) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (61) and (1994) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5739) aNaturalNumber0(sz10) = all_47_2_83
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (5739) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (61) aNaturalNumber0(sz10) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (831), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1830) and (2097) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5759) all_82_2_109 = all_18_1_20
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1830,5759) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1227) all_18_1_20 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1227,5759) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1830) all_82_2_109 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1830) and (2100) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (652), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1787) and (2031) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5752) all_37_2_63 = all_20_2_24
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1195,5752) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1787) all_20_2_24 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1787) and (2034) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (699), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2298) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5775) all_72_1_100 = all_20_0_22
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1244,5775) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1828) all_20_0_22 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2301) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (697), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2097) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5767) all_82_2_109 = all_72_1_100
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1830,5767) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1244) all_72_1_100 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1244,5767) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2100) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (556), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2105) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5791) all_72_3_102 = all_22_2_27
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1243,5791) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1788) all_22_2_27 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1788) and (2108) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (780), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1787) and (2366) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5783) all_37_3_64 = all_20_2_24
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1233,5783) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1787) all_20_2_24 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1787,5783) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1233) all_37_3_64 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1787) and (2369) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1010), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2446) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5805) all_39_8_74 = all_20_0_22
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1179,5805) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1828) all_20_0_22 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2449) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (603), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2105) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5798) all_52_1_86 = all_22_2_27
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1238,5798) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1788) all_22_2_27 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1788) and (2108) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (797), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2298) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5820) all_22_1_26 = all_20_0_22
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (5820,1229) yields a new equation:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2724) all_20_0_22 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Simplifying 2724 yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1828) all_20_0_22 = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2301) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (878), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1787) and (2366) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (5812) all_20_2_24 = all_14_1_14
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1787) and (2369) follows:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (896), into two cases.
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.59  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1790) and (1939) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5836) all_62_2_94 = all_12_1_11
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1790,5836) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1221) all_12_1_11 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1221,5836) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1790) all_62_2_94 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1790) and (1942) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (365), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (5464) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1775) and (1780) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5828) all_82_2_109 = all_22_2_27
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1830,5828) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1788) all_22_2_27 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1788,5828) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1830) and (5467) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (750), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1674) and (3035) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5849) all_52_2_87 = all_47_1_82
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1674,5849) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1237) all_47_1_82 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1237,5849) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1674) all_52_2_87 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1674) and (3038) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (768), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1281) and (1969) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5842) all_39_7_73 = all_12_0_10
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1236,5842) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1281) and (1972) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (668), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (2186) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5862) all_57_2_90 = all_26_1_32
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1789,5862) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1202) all_26_1_32 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1202,5862) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1789) all_57_2_90 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (2189) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (475), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2218)  ~ (aNaturalNumber0(all_0_9_9) = all_20_2_24)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2218) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (1284) and (2090) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2221) aNaturalNumber0(all_0_9_9) = all_20_2_24
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5855) all_24_2_30 = all_20_2_24
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1282,5855) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1787) all_20_2_24 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1787) and (2221) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (740), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1790) and (1939) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5876) all_62_2_94 = all_47_1_82
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1790,5876) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1237) all_47_1_82 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1237,5876) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1790) all_62_2_94 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1790) and (1942) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1079), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5866)  ~ (aNaturalNumber0(sz10) = all_16_2_18)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1225) and (5866) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (61) and (1994) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5869) aNaturalNumber0(sz10) = all_16_2_18
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1225) all_16_2_18 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1225) and (5869) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (61) aNaturalNumber0(sz10) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (681), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2171) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (5890) all_24_1_29 = all_20_0_22
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1207,5890) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1828) all_20_0_22 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (2174) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (598), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (2665) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (5882) all_67_2_97 = all_52_1_86
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1829,5882) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1238) all_52_1_86 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1238,5882) yields a new equation:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1829) and (2668) follows:
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (819), into two cases.
% 223.65/172.60  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1945) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (5905) all_57_2_90 = all_20_1_23
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1789,5905) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1228) all_20_1_23 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1228,5905) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1789) all_57_2_90 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1948) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (721), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1945) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (5897) all_67_1_96 = all_57_2_90
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1242,5897) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1789) all_57_2_90 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1789,5897) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1242) all_67_1_96 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1948) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (894), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2298) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5920) all_20_0_22 = all_12_1_11
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2301) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (821), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2366) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5913) all_20_1_23 = all_20_2_24
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1228,5913) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1787) all_20_2_24 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1787) and (2369) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (872), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1829) and (4124) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5932) all_67_2_97 = all_14_1_14
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1829,5932) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1218) all_14_1_14 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1218,5932) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1829) all_67_2_97 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1829) and (4127) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (467), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1284) and (2090) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1018), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (2552) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (5948) all_52_2_87 = all_39_8_74
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1674,5948) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1179) all_39_8_74 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1179,5948) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1674) all_52_2_87 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (2555) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (863), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2136) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (5940) all_24_0_28 = all_16_1_17
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1350) and (2139) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (895), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1791) and (1977) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (5962) all_72_2_101 = all_12_1_11
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1791,5962) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1221) all_12_1_11 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1221,5962) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1791) all_72_2_101 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1791) and (1980) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (769), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1674) and (3035) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5956) all_52_2_87 = all_39_7_73
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1674,5956) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1236) all_39_7_73 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1236,5956) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1674) all_52_2_87 = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1674) and (3038) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (816), into two cases.
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2298) follows:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5978) all_20_0_22 = all_20_1_23
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (5978,1828) yields a new equation:
% 223.65/172.61  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (11982) all_20_1_23 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Simplifying 11982 yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1228) all_20_1_23 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2301) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (591), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2159) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (5970) all_57_3_91 = all_47_2_83
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (2199,5970) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,5970) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2199) all_57_3_91 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2162) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (975), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1228) and (2055) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (5994) all_62_1_93 = all_20_1_23
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1240,5994) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1228) all_20_1_23 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1228,5994) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1240) all_62_1_93 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1228) and (2058) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1058), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2120) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (5986) all_67_2_97 = all_18_2_21
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1829,5986) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1226) all_18_2_21 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1226,5986) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1829) all_67_2_97 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1829) and (2123) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (621), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3339) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6010) all_77_2_105 = all_47_3_84
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,6010) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2191) all_47_3_84 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (2191,6010) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3342) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (526), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1787) and (2031) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6002) all_82_3_110 = all_20_2_24
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1247,6002) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1787) all_20_2_24 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1787,6002) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1247) all_82_3_110 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1787) and (2034) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (741), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1945) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6026) all_57_2_90 = all_47_1_82
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1789,6026) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1237) all_47_1_82 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1237,6026) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1789) all_57_2_90 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1789) and (1948) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (712), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1674) and (3035) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6018) all_72_1_100 = all_52_2_87
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1244,6018) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1674) all_52_2_87 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1674,6018) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1244) all_72_1_100 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1674) and (3038) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (541), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2031) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6042) all_77_3_106 = all_20_2_24
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1245,6042) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1787) all_20_2_24 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1787,6042) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1245) all_77_3_106 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2034) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (434), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6030)  ~ (aNaturalNumber0(all_0_8_8) = all_20_0_22)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (6030) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1351) and (2575) yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6033) aNaturalNumber0(all_0_8_8) = all_20_0_22
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6034) all_24_0_28 = all_20_0_22
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (6034,1350) yields a new equation:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2724) all_20_0_22 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Simplifying 2724 yields:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (6033) follows:
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (739), into two cases.
% 223.65/172.62  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (1977) follows:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6057) all_72_2_101 = all_47_1_82
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1791,6057) yields a new equation:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1237) all_47_1_82 = 0
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1237,6057) yields a new equation:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (1980) follows:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (962), into two cases.
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2061)  ~ (aNaturalNumber0(xn) = all_47_2_83)
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1293) and (2061) follows:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2064) aNaturalNumber0(xn) = all_47_2_83
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6050) all_62_1_93 = all_47_2_83
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1240,6050) yields a new equation:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1293) all_47_2_83 = 0
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1293) and (2064) follows:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (783), into two cases.
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1292) and (3485) follows:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.65/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6071) all_37_3_64 = all_16_0_16
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1233,6071) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1292) all_16_0_16 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1292,6071) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1233) all_37_3_64 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1292) and (3488) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (846), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (3035) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6065) all_52_2_87 = all_18_1_20
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1674,6065) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1227) all_18_1_20 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1227,6065) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1674) all_52_2_87 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (3038) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (1072), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1229) and (2891) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6087) all_22_1_26 = all_18_2_21
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1229) and (2894) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (904), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1283) and (3028) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6079) all_26_2_33 = all_12_1_11
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1283,6079) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1221) all_12_1_11 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1221,6079) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1283) all_26_2_33 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1283) and (3031) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (993), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (2552) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6103) all_57_1_89 = all_52_2_87
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (980,6103) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1674) all_52_2_87 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1674,6103) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (980) all_57_1_89 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (2555) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (736), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (2097) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6095) all_82_2_109 = all_47_1_82
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1830,6095) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1237) all_47_1_82 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1237,6095) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1830) all_82_2_109 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (2100) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (900), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (2275) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6119) all_77_2_105 = all_12_1_11
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1294,6119) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1221) all_12_1_11 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1221,6119) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (2278) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (859), into two cases.
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1787) and (2366) follows:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6111) all_20_2_24 = all_16_1_17
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (6111,1787) yields a new equation:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4239) all_16_1_17 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Simplifying 4239 yields:
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (848) all_16_1_17 = 0
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.63  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1787) and (2369) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1015), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1283) and (2252) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6133) all_39_8_74 = all_26_2_33
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1179,6133) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1283,6133) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1179) all_39_8_74 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1283) and (2255) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (361), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1788) and (2144) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1788) all_22_2_27 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1788) and (2147) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (316), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1829) and (2665) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1829) all_67_2_97 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1829) and (2668) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (757), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (1977) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6141) all_72_2_101 = all_39_7_73
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1791,6141) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1236) all_39_7_73 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1236,6141) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1791) and (1980) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (969), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1244) and (2604) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6163) all_72_1_100 = all_62_1_93
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1244,6163) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1240) all_62_1_93 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1240,6163) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1244) all_72_1_100 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1244) and (2607) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1046), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1236) and (2522) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6155) all_39_7_73 = all_37_4_65
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1236,6155) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1232) all_37_4_65 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1232,6155) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1236) all_39_7_73 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1236) and (2525) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1133), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2446) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6178) all_20_0_22 = all_12_2_12
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2449) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (442), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6167)  ~ (aNaturalNumber0(all_0_8_8) = all_16_0_16)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (6167) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1351) and (2575) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6170) aNaturalNumber0(all_0_8_8) = all_16_0_16
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6171) all_24_0_28 = all_16_0_16
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (6171,1350) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2760) all_16_0_16 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Simplifying 2760 yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1292) all_16_0_16 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (6170) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (539), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1789) and (2186) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6192) all_77_3_106 = all_57_2_90
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1245,6192) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1789) all_57_2_90 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1789,6192) yields a new equation:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1245) all_77_3_106 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1789) and (2189) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (890), into two cases.
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6182)  ~ (aNaturalNumber0(sz10) = all_12_1_11)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1221) and (6182) follows:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6185) aNaturalNumber0(sz10) = all_12_1_11
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1221) all_12_1_11 = 0
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.64  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1221) and (6185) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (457), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2326)  ~ (aNaturalNumber0(all_0_9_9) = all_77_2_105)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1294) and (2326) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1284) and (2090) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2329) aNaturalNumber0(all_0_9_9) = all_77_2_105
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6208) all_77_2_105 = all_26_2_33
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1294,6208) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1283) all_26_2_33 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1283,6208) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1294) all_77_2_105 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1294) and (2329) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (838), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1787) and (2366) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6200) all_20_2_24 = all_18_1_20
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1787) and (2369) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1117), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2604)  ~ (aNaturalNumber0(xn) = all_72_1_100)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1244) and (2604) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2607) aNaturalNumber0(xn) = all_72_1_100
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6222) all_72_1_100 = all_14_2_15
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1244,6222) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1200) all_14_2_15 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1200,6222) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1244) all_72_1_100 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1244) and (2607) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (320), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6212)  ~ (aNaturalNumber0(sz00) = all_67_2_97)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1829) and (6212) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (26) and (2070) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6215) aNaturalNumber0(sz00) = all_67_2_97
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1829) all_67_2_97 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1829) and (6215) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (26) aNaturalNumber0(sz00) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (451), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2178)  ~ (aNaturalNumber0(all_0_9_9) = all_20_0_22)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2178) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1284) and (2090) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2181) aNaturalNumber0(all_0_9_9) = all_20_0_22
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6236) all_26_2_33 = all_20_0_22
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1283,6236) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1828) all_20_0_22 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1828,6236) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1283) all_26_2_33 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2181) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1125), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (848) and (2268) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6230) all_16_1_17 = all_14_2_15
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (848,6230) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1200) all_14_2_15 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1200,6230) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (848) all_16_1_17 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (848) and (2271) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1033), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (2120) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6250) all_67_2_97 = all_37_4_65
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1829,6250) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1232) all_37_4_65 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1232,6250) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (2123) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (794), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6240)  ~ (aNaturalNumber0(sz00) = all_22_1_26)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1229) and (6240) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (26) and (2070) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6243) aNaturalNumber0(sz00) = all_22_1_26
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1229) all_22_1_26 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1229) and (6243) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (311), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2151) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2154) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (857), into two cases.
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1945) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6258) all_57_2_90 = all_16_1_17
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1789,6258) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (848) all_16_1_17 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (848,6258) yields a new equation:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1789) all_57_2_90 = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1789) and (1948) follows:
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.77/172.65  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (832), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4124) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (12) and (1940) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6280) all_67_2_97 = all_18_1_20
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,6280) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1227) all_18_1_20 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1227,6280) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (4127) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (12) aNaturalNumber0(xm) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (949), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1229) and (2891) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6272) all_77_1_104 = all_22_1_26
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1246,6272) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1229) all_22_1_26 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1229,6272) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1246) all_77_1_104 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1229) and (2894) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (369), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6292)  ~ (aNaturalNumber0(xr) = all_20_2_24)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (6292) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (88) and (8229) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6295) aNaturalNumber0(xr) = all_20_2_24
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1787) all_20_2_24 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1787) and (6295) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (88) aNaturalNumber0(xr) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (860), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1294) and (2275) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2278) aNaturalNumber0(xm) = all_77_2_105
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6288) all_77_2_105 = all_16_1_17
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1294,6288) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (848) all_16_1_17 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (848,6288) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1294) all_77_2_105 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1294) and (2278) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1066), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (2552) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6308) all_52_2_87 = all_18_2_21
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1674,6308) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1226) all_18_2_21 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1226,6308) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1674) all_52_2_87 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1674) and (2555) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (446), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6298)  ~ (aNaturalNumber0(sz10) = all_26_2_33)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1283) and (6298) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (61) and (1994) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6301) aNaturalNumber0(sz10) = all_26_2_33
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1283) all_26_2_33 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1283) and (6301) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (61) aNaturalNumber0(sz10) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (948), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1233) and (3295) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6324) all_77_1_104 = all_37_3_64
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1246,6324) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1233) all_37_3_64 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1233,6324) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1246) all_77_1_104 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1233) and (3298) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (489), into two cases.
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6312)  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (6312) follows:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1284) and (2090) yields:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6315) aNaturalNumber0(all_0_9_9) = all_67_2_97
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6316) all_67_2_97 = all_12_0_10
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,6316) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1281,6316) yields a new equation:
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.66  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (6315) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (502), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (3035) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1674) all_52_2_87 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1674) and (3038) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (331), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6328)  ~ (aNaturalNumber0(xr) = all_72_2_101)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1791) and (6328) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (88) and (8229) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6331) aNaturalNumber0(xr) = all_72_2_101
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1791) all_72_2_101 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1791) and (6331) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (88) aNaturalNumber0(xr) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (922), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1242) and (2334) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6350) all_82_1_108 = all_67_1_96
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1249,6350) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1242) all_67_1_96 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1242,6350) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1249) all_82_1_108 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1242) and (2337) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (447), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6340)  ~ (aNaturalNumber0(sz00) = all_26_2_33)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1283) and (6340) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (26) and (2070) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6343) aNaturalNumber0(sz00) = all_26_2_33
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1283) all_26_2_33 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1283) and (6343) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (26) aNaturalNumber0(sz00) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1099), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1227) and (1933) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6366) all_18_1_20 = all_16_2_18
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1227,6366) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1225) all_16_2_18 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1225,6366) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1227) all_18_1_20 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1227) and (1936) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (707), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1292) and (3485) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6358) all_72_1_100 = all_16_0_16
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1244,6358) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1292) all_16_0_16 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1292,6358) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1244) all_72_1_100 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1292) and (3488) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1007), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6376)  ~ (aNaturalNumber0(sz00) = all_39_8_74)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1179) and (6376) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (26) and (2070) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6379) aNaturalNumber0(sz00) = all_39_8_74
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1179) all_39_8_74 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1179) and (6379) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (26) aNaturalNumber0(sz00) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1091), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1674) and (2552) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6374) all_52_2_87 = all_16_2_18
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1674,6374) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1225) all_16_2_18 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1225,6374) yields a new equation:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1674) all_52_2_87 = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1674) and (2555) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (432), into two cases.
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6390)  ~ (aNaturalNumber0(all_0_8_8) = all_82_2_109)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (6390) follows:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1351) and (2575) yields:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.77/172.67  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6393) aNaturalNumber0(all_0_8_8) = all_82_2_109
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6394) all_82_2_109 = all_24_0_28
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1830,6394) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1350) all_24_0_28 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1350,6394) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1830) all_82_2_109 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (6393) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1039), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1283) and (2252) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6386) all_37_4_65 = all_26_2_33
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1232,6386) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1283) all_26_2_33 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1283,6386) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1232) all_37_4_65 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1283) and (2255) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (569), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (2642) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6410) all_72_2_101 = all_67_3_98
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1791,6410) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1241) all_67_3_98 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1241,6410) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1791) and (2645) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1053), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1221) and (2081) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2084) aNaturalNumber0(xn) = all_12_1_11
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6402) all_37_4_65 = all_12_1_11
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1232,6402) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1221) all_12_1_11 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1221,6402) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1232) all_37_4_65 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1221) and (2084) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (935), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (2120) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6426) all_77_1_104 = all_67_2_97
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1246,6426) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1829) all_67_2_97 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1829,6426) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1246) all_77_1_104 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (2123) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (944), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (2552) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6418) all_77_1_104 = all_52_2_87
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1246,6418) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1674) all_52_2_87 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1674,6418) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1246) all_77_1_104 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1674) and (2555) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (550), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2112) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6442) all_82_2_109 = all_72_3_102
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1830,6442) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1243) all_72_3_102 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1243,6442) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1830) all_82_2_109 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2115) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (491), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5216)  ~ (aNaturalNumber0(all_0_9_9) = all_72_2_101)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1791) and (5216) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1284) and (2090) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5219) aNaturalNumber0(all_0_9_9) = all_72_2_101
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6434) all_72_2_101 = all_12_0_10
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1791,6434) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1281) all_12_0_10 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1281,6434) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1791) all_72_2_101 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1791) and (5219) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (337), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (5464) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1775) and (1780) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6458) all_82_2_109 = all_72_2_101
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1830,6458) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1791) all_72_2_101 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1791,6458) yields a new equation:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1830) all_82_2_109 = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1830) and (5467) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (959), into two cases.
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1829) and (2120) follows:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6450) all_67_2_97 = all_62_1_93
% 223.77/172.68  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1829,6450) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1240) all_62_1_93 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1240,6450) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1829) all_67_2_97 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1829) and (2123) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (505), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6470)  ~ (aNaturalNumber0(xk) = all_67_2_97)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (6470) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1665) and (1670) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6473) aNaturalNumber0(xk) = all_67_2_97
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6474) all_67_2_97 = all_52_2_87
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1829,6474) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1674) all_52_2_87 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1674,6474) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1829) all_67_2_97 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1829) and (6473) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1665) aNaturalNumber0(xk) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (759), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1789) and (1945) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6466) all_57_2_90 = all_39_7_73
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1789,6466) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1236) all_39_7_73 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1236,6466) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1789) all_57_2_90 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1789) and (1948) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (908), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6486)  ~ (aNaturalNumber0(sz10) = all_82_1_108)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1249) and (6486) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (61) and (1994) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6489) aNaturalNumber0(sz10) = all_82_1_108
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1249) all_82_1_108 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1249) and (6489) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (61) aNaturalNumber0(sz10) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (630), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2112) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6482) all_82_2_109 = all_39_6_72
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1830,6482) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (629) all_39_6_72 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (629,6482) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1830) and (2115) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (633), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (2642) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6504) all_72_2_101 = all_39_6_72
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1791,6504) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (629) all_39_6_72 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (629,6504) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1791) all_72_2_101 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1791) and (2645) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (558), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1294) and (3339) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6496) all_77_2_105 = all_72_3_102
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1294,6496) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1243) all_72_3_102 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1243,6496) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1294) all_77_2_105 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1294) and (3342) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1149), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1933)  ~ (aNaturalNumber0(xn) = all_18_1_20)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1227) and (1933) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1936) aNaturalNumber0(xn) = all_18_1_20
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6520) all_18_1_20 = all_12_2_12
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1227,6520) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1223) all_12_2_12 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1223,6520) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1227) all_18_1_20 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1227) and (1936) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (523), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (2506) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6512) all_82_3_110 = all_62_2_94
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1247,6512) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1790) all_62_2_94 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1790,6512) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1247) all_82_3_110 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (2509) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (893), into two cases.
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1829) and (4124) follows:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6536) all_67_2_97 = all_12_1_11
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1829,6536) yields a new equation:
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1221) all_12_1_11 = 0
% 223.77/172.69  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1221,6536) yields a new equation:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1829) all_67_2_97 = 0
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1829) and (4127) follows:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1145), into two cases.
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1236) and (2522) follows:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6528) all_39_7_73 = all_12_2_12
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1236,6528) yields a new equation:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1223) all_12_2_12 = 0
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1223,6528) yields a new equation:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1236) all_39_7_73 = 0
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1236) and (2525) follows:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (906), into two cases.
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (1969) follows:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.77/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6552) all_12_0_10 = all_12_1_11
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1281) and (1972) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (493), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2558)  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1789) and (2558) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1284) and (2090) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2561) aNaturalNumber0(all_0_9_9) = all_57_2_90
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6544) all_57_2_90 = all_12_0_10
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1789,6544) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1281) all_12_0_10 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1281,6544) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1789) all_57_2_90 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1789) and (2561) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (593), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1350) and (2899) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6568) all_57_3_91 = all_24_0_28
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (2199,6568) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1350) all_24_0_28 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1350,6568) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2199) all_57_3_91 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1350) and (2902) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (814), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (2097) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6560) all_82_2_109 = all_20_1_23
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1830,6560) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1228) all_20_1_23 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1228,6560) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1830) all_82_2_109 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (2100) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (537), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1791) and (2642) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6582) all_77_3_106 = all_72_2_101
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1245,6582) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1791) all_72_2_101 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1791,6582) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1245) all_77_3_106 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1791) and (2645) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (826), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (3035) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6576) all_52_2_87 = all_20_1_23
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1674,6576) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1228) all_20_1_23 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1228,6576) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1674) all_52_2_87 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1674) and (3038) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (566), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1830) and (2112) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6596) all_82_2_109 = all_67_3_98
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1830,6596) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1241) all_67_3_98 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1241,6596) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1830) all_82_2_109 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1830) and (2115) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (820), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1788) and (2144) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6590) all_22_2_27 = all_20_1_23
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1788) and (2147) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (700), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1791) and (1977) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6610) all_72_1_100 = all_72_2_101
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1244,6610) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1791) all_72_2_101 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1791,6610) yields a new equation:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1244) all_72_1_100 = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1791) and (1980) follows:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (818), into two cases.
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.88/172.70  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1790) and (1939) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6604) all_62_2_94 = all_20_1_23
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1790,6604) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1228) all_20_1_23 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1228,6604) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1790) all_62_2_94 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1790) and (1942) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (309), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2112) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2115) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (852), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2097) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6618) all_82_2_109 = all_16_1_17
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1830,6618) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (848) all_16_1_17 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (848,6618) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1830) all_82_2_109 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1830) and (2100) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (508), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6636)  ~ (aNaturalNumber0(xk) = all_62_2_94)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (6636) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1665) and (1670) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6639) aNaturalNumber0(xk) = all_62_2_94
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6640) all_62_2_94 = all_52_2_87
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1790,6640) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1674) all_52_2_87 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1674,6640) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1790) all_62_2_94 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1790) and (6639) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1665) aNaturalNumber0(xk) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (347), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5480) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1775) and (1780) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6632) all_67_2_97 = all_62_2_94
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,6632) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1790) all_62_2_94 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1790,6632) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5483) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (958), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (2151) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6654) all_82_2_109 = all_62_1_93
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1830,6654) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1240) all_62_1_93 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1240,6654) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1830) all_82_2_109 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (2154) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (333), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1977)  ~ (aNaturalNumber0(xm) = all_72_2_101)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (1977) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1980) aNaturalNumber0(xm) = all_72_2_101
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (1980) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (552), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2171) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6668) all_72_3_102 = all_20_0_22
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1243,6668) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1828,6668) yields a new equation:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1243) all_72_3_102 = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1828) and (2174) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (340), into two cases.
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6658)  ~ (aNaturalNumber0(xr) = all_62_2_94)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (6658) follows:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (88) and (8229) yields:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.88/172.71  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6661) aNaturalNumber0(xr) = all_62_2_94
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1790) all_62_2_94 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (6661) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (88) aNaturalNumber0(xr) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (308), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6680)  ~ (aNaturalNumber0(xr) = all_82_2_109)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (6680) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (88) and (8229) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6683) aNaturalNumber0(xr) = all_82_2_109
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1830) all_82_2_109 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (6683) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (88) aNaturalNumber0(xr) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (646), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2665) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6676) all_67_2_97 = all_37_2_63
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1829,6676) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1195) all_37_2_63 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1195,6676) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1829) all_67_2_97 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1829) and (2668) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (654), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2159) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6698) all_47_2_83 = all_37_2_63
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1293,6698) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1195) all_37_2_63 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1195,6698) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1293) all_47_2_83 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1293) and (2162) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1081), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (2151) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (91) and (1934) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6690) all_82_2_109 = all_16_2_18
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1830,6690) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1225) all_16_2_18 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1225,6690) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1830) all_82_2_109 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1830) and (2154) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (91) aNaturalNumber0(xn) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1034), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2446) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6714) all_37_4_65 = all_20_0_22
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1232,6714) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1828) all_20_0_22 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1828,6714) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1232) all_37_4_65 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2449) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (91) aNaturalNumber0(xn) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (638), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (3339) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6706) all_77_2_105 = all_39_6_72
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1294,6706) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (629) all_39_6_72 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (629,6706) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1294) all_77_2_105 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1294) and (3342) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (538), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2506)  ~ (aNaturalNumber0(xp) = all_62_2_94)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1790) and (2506) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2509) aNaturalNumber0(xp) = all_62_2_94
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6730) all_77_3_106 = all_62_2_94
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1245,6730) yields a new equation:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1790) all_62_2_94 = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1790) and (2509) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1111), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1292) and (2984) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6722) all_16_0_16 = all_14_2_15
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1292) and (2987) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (773), into two cases.
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2097) follows:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2100) aNaturalNumber0(xm) = all_82_2_109
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6745) all_82_2_109 = all_37_3_64
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.72  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1830,6745) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1233) all_37_3_64 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1233,6745) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1830) all_82_2_109 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1830) and (2100) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1017), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1281) and (2374) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6737) all_39_8_74 = all_12_0_10
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1179,6737) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1281) all_12_0_10 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1281,6737) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1179) all_39_8_74 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1281) and (2377) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (620), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2031) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6759) all_47_3_84 = all_20_2_24
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (2191,6759) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1787) all_20_2_24 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1787,6759) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2191) all_47_3_84 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1787) and (2034) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1126), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3165)  ~ (aNaturalNumber0(xn) = all_14_1_14)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1218) and (3165) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (91) and (1934) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3168) aNaturalNumber0(xn) = all_14_1_14
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6753) all_14_1_14 = all_14_2_15
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1218) and (3168) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (91) aNaturalNumber0(xn) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (555), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1789) and (2186) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6773) all_72_3_102 = all_57_2_90
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1243,6773) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1789) all_57_2_90 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1789,6773) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1243) all_72_3_102 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1789) and (2189) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (932), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6763)  ~ (aNaturalNumber0(sz10) = all_77_1_104)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1246) and (6763) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (61) and (1994) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6766) aNaturalNumber0(sz10) = all_77_1_104
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1246) all_77_1_104 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1246) and (6766) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (61) aNaturalNumber0(sz10) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (815), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (4124) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6789) all_67_2_97 = all_20_1_23
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1829,6789) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1228) all_20_1_23 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1228,6789) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1829) all_67_2_97 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (4127) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (676), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1282) and (2475) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6781) all_26_1_32 = all_24_2_30
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1202,6781) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1282) all_24_2_30 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1282,6781) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1202) all_26_1_32 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1282) and (2478) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (684), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2186)  ~ (aNaturalNumber0(xp) = all_57_2_90)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1789) and (2186) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2189) aNaturalNumber0(xp) = all_57_2_90
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6805) all_57_2_90 = all_24_1_29
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1789,6805) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1207) all_24_1_29 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1207,6805) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1789) all_57_2_90 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1789) and (2189) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (840), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2962) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6797) all_47_2_83 = all_18_1_20
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1293,6797) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1227) all_18_1_20 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1227,6797) yields a new equation:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2965) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (589), into two cases.
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2031) follows:
% 223.88/172.73  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6821) all_57_3_91 = all_20_2_24
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (2199,6821) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1787) all_20_2_24 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1787) and (2034) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (766), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (3028) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6813) all_39_7_73 = all_26_2_33
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1236,6813) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1283) all_26_2_33 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1283,6813) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1236) all_39_7_73 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1283) and (3031) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (632), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2171) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6835) all_39_6_72 = all_20_0_22
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (629,6835) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1828) all_20_0_22 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2174) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (514), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6824)  ~ (aNaturalNumber0(xk) = all_16_0_16)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (6824) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1665) and (1670) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6827) aNaturalNumber0(xk) = all_16_0_16
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6828) all_52_2_87 = all_16_0_16
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1674,6828) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1292) all_16_0_16 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (6827) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1665) aNaturalNumber0(xk) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (323), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6844)  ~ (aNaturalNumber0(xr) = all_20_0_22)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1828) and (6844) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (8229)  ~ (aNaturalNumber0(xr) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (88) and (8229) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6847) aNaturalNumber0(xr) = all_20_0_22
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1828) all_20_0_22 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (957), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6838)  ~ (aNaturalNumber0(sz00) = all_62_1_93)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1240) and (6838) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (26) and (2070) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6841) aNaturalNumber0(sz00) = all_62_1_93
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1240) all_62_1_93 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1240) and (6841) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (746), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (2136) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6862) all_47_1_82 = all_24_0_28
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1237,6862) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1350) all_24_0_28 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1350,6862) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1237) all_47_1_82 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1350) and (2139) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (999), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2891)  ~ (aNaturalNumber0(xn) = all_22_1_26)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1229) and (2891) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2894) aNaturalNumber0(xn) = all_22_1_26
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6854) all_57_1_89 = all_22_1_26
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (980,6854) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1229) all_22_1_26 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1229,6854) yields a new equation:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (980) all_57_1_89 = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1229) and (2894) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1146), into two cases.
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3295)  ~ (aNaturalNumber0(xn) = all_37_3_64)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1233) and (3295) follows:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (3298) aNaturalNumber0(xn) = all_37_3_64
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6878) all_37_3_64 = all_12_2_12
% 223.88/172.74  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1233,6878) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1223) all_12_2_12 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1223,6878) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1233) all_37_3_64 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1233) and (3298) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (417), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4548)  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (4548) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1295) and (2129) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4551) aNaturalNumber0(all_0_7_7) = all_67_2_97
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6870) all_67_2_97 = all_16_0_16
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,6870) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1292) all_16_0_16 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1292,6870) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (4551) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (355), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5464)  ~ (aNaturalNumber0(all_0_3_3) = all_82_2_109)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (5464) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1775) and (1780) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (5467) aNaturalNumber0(all_0_3_3) = all_82_2_109
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (6890) all_82_2_109 = all_57_2_90
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1830,6890) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1789) all_57_2_90 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1789,6890) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1830) all_82_2_109 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1830) and (5467) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (501), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (1665) and (1670) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1665) aNaturalNumber0(xk) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1674) all_52_2_87 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (1006), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6902)  ~ (aNaturalNumber0(sz10) = all_39_8_74)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1179) and (6902) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (61) and (1994) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (6905) aNaturalNumber0(sz10) = all_39_8_74
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1179) all_39_8_74 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1179) and (6905) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (61) aNaturalNumber0(sz10) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (623), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1292) and (2023) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (9) and (2008) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (6898) all_47_3_84 = all_16_0_16
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (2191,6898) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1292) all_16_0_16 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1292,6898) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2191) all_47_3_84 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1292) and (2026) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (9) aNaturalNumber0(xp) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (436), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6916)  ~ (aNaturalNumber0(all_0_8_8) = all_62_2_94)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (6916) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1351) and (2575) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6919) aNaturalNumber0(all_0_8_8) = all_62_2_94
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (6920) all_62_2_94 = all_24_0_28
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (6920,1790) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5715) all_24_0_28 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Simplifying 5715 yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1350) all_24_0_28 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1790) and (6919) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (782), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2962) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (6912) all_47_2_83 = all_37_3_64
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1293,6912) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1233) all_37_3_64 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1233,6912) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1293) all_47_2_83 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2965) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1113), into two cases.
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (2252) follows:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (6936) all_26_2_33 = all_14_2_15
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,6936) yields a new equation:
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1200) all_14_2_15 = 0
% 223.88/172.75  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1200,6936) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (2255) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (710), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1282) and (2382) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (6928) all_72_1_100 = all_24_2_30
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1244,6928) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1282) all_24_2_30 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1282,6928) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1244) all_72_1_100 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1282) and (2385) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (869), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6946)  ~ (aNaturalNumber0(sz10) = all_14_1_14)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1218) and (6946) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (61) and (1994) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (6949) aNaturalNumber0(sz10) = all_14_1_14
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1218) all_14_1_14 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1218) and (6949) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (61) aNaturalNumber0(sz10) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (727), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (2136) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (12) and (1940) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (6942) all_67_1_96 = all_24_0_28
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1242,6942) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1350) all_24_0_28 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1350,6942) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1242) all_67_1_96 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (2139) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (12) aNaturalNumber0(xm) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (885), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (1969) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6962) all_14_1_14 = all_12_0_10
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (6962,1218) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2959) all_12_0_10 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Simplifying 2959 yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1281) all_12_0_10 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1281) and (1972) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1031), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6952)  ~ (aNaturalNumber0(sz00) = all_37_4_65)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1232) and (6952) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (26) and (2070) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (6955) aNaturalNumber0(sz00) = all_37_4_65
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1232) all_37_4_65 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1232) and (6955) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (26) aNaturalNumber0(sz00) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1074), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (848) and (2268) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6977) all_18_2_21 = all_16_1_17
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (6977,1226) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4239) all_16_1_17 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Simplifying 4239 yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (848) all_16_1_17 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (848) and (2271) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (626), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2475) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (6970) all_47_3_84 = all_24_2_30
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (2191,6970) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1282) all_24_2_30 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1282) and (2478) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (366), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (5480) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1775) and (1780) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (6991) all_67_2_97 = all_22_2_27
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1829,6991) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1788,6991) yields a new equation:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1829) all_67_2_97 = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1829) and (5483) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (658), into two cases.
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2475) follows:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (6984) all_37_2_63 = all_24_2_30
% 223.88/172.76  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1195,6984) yields a new equation:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2478) follows:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (487), into two cases.
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (1284) and (2090) yields:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1281) all_12_0_10 = 0
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (990), into two cases.
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2252)  ~ (aNaturalNumber0(xn) = all_26_2_33)
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (2252) follows:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2255) aNaturalNumber0(xn) = all_26_2_33
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (6999) all_57_1_89 = all_26_2_33
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (980,6999) yields a new equation:
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1283) all_26_2_33 = 0
% 223.88/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1283,6999) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (980) all_57_1_89 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1283) and (2255) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (488), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2290)  ~ (aNaturalNumber0(all_0_9_9) = all_82_2_109)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2290) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1284) and (2090) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2293) aNaturalNumber0(all_0_9_9) = all_82_2_109
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7019) all_82_2_109 = all_12_0_10
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1830,7019) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1281) all_12_0_10 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1281,7019) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2293) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1098), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1228) and (2055) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7011) all_20_1_23 = all_16_2_18
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1228,7011) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1225) all_16_2_18 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1225,7011) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1228) all_20_1_23 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1228) and (2058) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (665), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2171) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7035) all_26_1_32 = all_20_0_22
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (7035,1202) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2724) all_20_0_22 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Simplifying 2724 yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1828) all_20_0_22 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1828) and (2174) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (702), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (1945) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7027) all_72_1_100 = all_57_2_90
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1244,7027) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1789) all_57_2_90 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1789,7027) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1244) all_72_1_100 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (1948) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (516), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7046)  ~ (aNaturalNumber0(xk) = all_26_2_33)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1283) and (7046) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1665) and (1670) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7049) aNaturalNumber0(xk) = all_26_2_33
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7050) all_52_2_87 = all_26_2_33
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1674,7050) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1283,7050) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1674) all_52_2_87 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (722), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2144) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7042) all_67_1_96 = all_22_2_27
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1242,7042) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1788) all_22_2_27 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1788,7042) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1242) all_67_1_96 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1788) and (2147) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (453), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4821)  ~ (aNaturalNumber0(all_0_9_9) = all_62_2_94)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1790) and (4821) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1284) and (2090) yields:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4824) aNaturalNumber0(all_0_9_9) = all_62_2_94
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7064) all_62_2_94 = all_26_2_33
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1790,7064) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1283) all_26_2_33 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1283,7064) yields a new equation:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1790) all_62_2_94 = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1790) and (4824) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1013), into two cases.
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2984) follows:
% 223.95/172.77  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7057) all_39_8_74 = all_16_0_16
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1179,7057) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1292) all_16_0_16 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2987) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1011), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (1953) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7080) all_77_2_105 = all_39_8_74
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,7080) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1179) all_39_8_74 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1179,7080) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (1956) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (743), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1787) and (2366) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (12) and (1940) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7072) all_47_1_82 = all_20_2_24
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1237,7072) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1787) all_20_2_24 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1787,7072) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1237) all_47_1_82 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1787) and (2369) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (12) aNaturalNumber0(xm) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (864), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1283) and (3028) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (12) and (1940) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7096) all_26_2_33 = all_16_1_17
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1283,7096) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (848) all_16_1_17 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (848,7096) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1283) all_26_2_33 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1283) and (3031) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (12) aNaturalNumber0(xm) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1112), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (1985) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (91) and (1934) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7088) all_24_0_28 = all_14_2_15
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1350,7088) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1200) all_14_2_15 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1200,7088) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1350) all_24_0_28 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1350) and (1988) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (91) aNaturalNumber0(xn) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (920), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2552)  ~ (aNaturalNumber0(xn) = all_52_2_87)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1674) and (2552) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2555) aNaturalNumber0(xn) = all_52_2_87
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7110) all_82_1_108 = all_52_2_87
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1249,7110) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1674) all_52_2_87 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1674,7110) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1249) all_82_1_108 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1674) and (2555) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (334), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7100)  ~ (aNaturalNumber0(sz10) = all_72_2_101)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1791) and (7100) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (61) and (1994) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7103) aNaturalNumber0(sz10) = all_72_2_101
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1791) all_72_2_101 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1791) and (7103) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (61) aNaturalNumber0(sz10) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (884), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (2382) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7124) all_24_2_30 = all_14_1_14
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1282,7124) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1218) all_14_1_14 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1218,7124) yields a new equation:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (2385) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (335), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7114)  ~ (aNaturalNumber0(sz00) = all_72_2_101)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (7114) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (26) and (2070) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7117) aNaturalNumber0(sz00) = all_72_2_101
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1791) all_72_2_101 = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1791) and (7117) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (26) aNaturalNumber0(sz00) = 0
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (392), into two cases.
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2620)  ~ (aNaturalNumber0(all_0_7_7) = all_22_2_27)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (2620) follows:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1295) and (2129) yields:
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.78  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2623) aNaturalNumber0(all_0_7_7) = all_22_2_27
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7136) all_77_2_105 = all_22_2_27
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1294,7136) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1788) all_22_2_27 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1788,7136) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1294) all_77_2_105 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (2623) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (336), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1775) and (1780) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1791) all_72_2_101 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (380), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1294) and (3339) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1294) all_77_2_105 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1294) and (3342) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (345), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1775) and (1780) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1775) aNaturalNumber0(all_0_3_3) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1790) all_62_2_94 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (961), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1294) and (1953) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1956) aNaturalNumber0(xn) = all_77_2_105
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7162) all_77_2_105 = all_62_1_93
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1294,7162) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1240) all_62_1_93 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1240,7162) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1294) all_77_2_105 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1294) and (1956) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (575), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2159) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7154) all_67_3_98 = all_47_2_83
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1241,7154) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,7154) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1241) all_67_3_98 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2162) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (725), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2962) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7178) all_67_1_96 = all_47_2_83
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1242,7178) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1293,7178) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1242) all_67_1_96 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2965) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (576), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2023) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7170) all_67_3_98 = all_16_0_16
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1241,7170) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1292) all_16_0_16 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1292,7170) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1241) all_67_3_98 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1292) and (2026) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (450), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6312)  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (6312) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (1284) and (2090) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (6315) aNaturalNumber0(all_0_9_9) = all_67_2_97
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7194) all_67_2_97 = all_26_2_33
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1829,7194) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1283) all_26_2_33 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1283,7194) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (6315) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (579), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1282) and (2475) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7186) all_67_3_98 = all_24_2_30
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1241,7186) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1282) all_24_2_30 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1282,7186) yields a new equation:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1241) all_67_3_98 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1282) and (2478) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (462), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2475) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1282) all_24_2_30 = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1282) and (2478) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (580), into two cases.
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1281) and (2039) follows:
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.79  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7202) all_67_3_98 = all_12_0_10
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1241,7202) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1281) all_12_0_10 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1281,7202) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1241) all_67_3_98 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1281) and (2042) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (474), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2312)  ~ (aNaturalNumber0(all_0_9_9) = all_22_2_27)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2312) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (1284) and (2090) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2315) aNaturalNumber0(all_0_9_9) = all_22_2_27
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7224) all_24_2_30 = all_22_2_27
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1282,7224) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2315) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (875), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1939)  ~ (aNaturalNumber0(xm) = all_62_2_94)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (1939) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (12) and (1940) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1942) aNaturalNumber0(xm) = all_62_2_94
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7216) all_62_2_94 = all_14_1_14
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1790,7216) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1218) all_14_1_14 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1218,7216) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1790) all_62_2_94 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1790) and (1942) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (12) aNaturalNumber0(xm) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (444), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (3028) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3031) aNaturalNumber0(xm) = all_26_2_33
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1283) all_26_2_33 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (3031) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (825), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (1969) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7231) all_20_1_23 = all_12_0_10
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1228,7231) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1281,7231) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1228) all_20_1_23 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (1972) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (439), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7248)  ~ (aNaturalNumber0(all_0_8_8) = all_20_2_24)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1787) and (7248) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (1351) and (2575) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7251) aNaturalNumber0(all_0_8_8) = all_20_2_24
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7252) all_24_0_28 = all_20_2_24
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1350,7252) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1787) all_20_2_24 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1787) and (7251) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1351) aNaturalNumber0(all_0_8_8) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (779), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1788) and (2144) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7245) all_37_3_64 = all_22_2_27
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1233,7245) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1788) all_22_2_27 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1788) and (2147) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (435), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7263)  ~ (aNaturalNumber0(all_0_8_8) = all_72_2_101)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1791) and (7263) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2575)  ~ (aNaturalNumber0(all_0_8_8) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (1351) and (2575) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7266) aNaturalNumber0(all_0_8_8) = all_72_2_101
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7267) all_72_2_101 = all_24_0_28
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1791,7267) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1350) all_24_0_28 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1350,7267) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1791) all_72_2_101 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (599), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2171) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (9) and (2008) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7259) all_52_1_86 = all_20_0_22
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1238,7259) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1828) all_20_0_22 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1828,7259) yields a new equation:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1238) all_52_1_86 = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (2174) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (9) aNaturalNumber0(xp) = 0
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (805), into two cases.
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1292) and (3485) follows:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.95/172.80  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7274) all_22_1_26 = all_16_0_16
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1229,7274) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1292) and (3488) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (426), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1350) and (2899) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1350) all_24_0_28 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1350) and (2902) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (404), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4226)  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1791) and (4226) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (1295) and (2129) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (4229) aNaturalNumber0(all_0_7_7) = all_72_2_101
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7281) all_72_2_101 = all_47_2_83
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1791,7281) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1293,7281) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1791) all_72_2_101 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1791) and (4229) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (429), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7299)  ~ (aNaturalNumber0(sz10) = all_24_0_28)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (7299) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (61) and (1994) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7302) aNaturalNumber0(sz10) = all_24_0_28
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1350) all_24_0_28 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (7302) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (61) aNaturalNumber0(sz10) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (858), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1788) and (2144) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7295) all_22_2_27 = all_16_1_17
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (7295,1788) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (4239) all_16_1_17 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Simplifying 4239 yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (848) all_16_1_17 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1788) and (2147) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (385), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1295) and (2129) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (469), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6312)  ~ (aNaturalNumber0(all_0_9_9) = all_67_2_97)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1829) and (6312) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1284) and (2090) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (6315) aNaturalNumber0(all_0_9_9) = all_67_2_97
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7309) all_67_2_97 = all_24_2_30
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1829,7309) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1282) all_24_2_30 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1282,7309) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1829) all_67_2_97 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1829) and (6315) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1284) aNaturalNumber0(all_0_9_9) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (387), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4548)  ~ (aNaturalNumber0(all_0_7_7) = all_67_2_97)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1829) and (4548) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1295) and (2129) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (4551) aNaturalNumber0(all_0_7_7) = all_67_2_97
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7328) all_77_2_105 = all_67_2_97
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1294,7328) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1829) all_67_2_97 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1829,7328) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1294) all_77_2_105 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1829) and (4551) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1025), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1228) and (2055) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (91) and (1934) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2058) aNaturalNumber0(xn) = all_20_1_23
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7321) all_39_8_74 = all_20_1_23
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1179,7321) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1228) all_20_1_23 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1228) and (2058) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (91) aNaturalNumber0(xn) = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (403), into two cases.
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2128)  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2128) follows:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1295) and (2129) yields:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2131) aNaturalNumber0(all_0_7_7) = all_20_0_22
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7342) all_47_2_83 = all_20_0_22
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1293,7342) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1828,7342) yields a new equation:
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1293) all_47_2_83 = 0
% 223.95/172.81  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1828) and (2131) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (351), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1945)  ~ (aNaturalNumber0(xm) = all_57_2_90)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1789) and (1945) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1948) aNaturalNumber0(xm) = all_57_2_90
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1789) and (1948) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (396), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1293) and (2962) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2965) aNaturalNumber0(xm) = all_47_2_83
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1293) all_47_2_83 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1293) and (2965) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (318), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2120)  ~ (aNaturalNumber0(xn) = all_67_2_97)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (2120) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2123) aNaturalNumber0(xn) = all_67_2_97
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1829) all_67_2_97 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (2123) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (390), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2755)  ~ (aNaturalNumber0(all_0_7_7) = all_62_2_94)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (2755) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1295) and (2129) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2758) aNaturalNumber0(all_0_7_7) = all_62_2_94
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7370) all_77_2_105 = all_62_2_94
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1294,7370) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1790) all_62_2_94 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1790,7370) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1294) all_77_2_105 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1790) and (2758) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (551), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2665)  ~ (aNaturalNumber0(xp) = all_67_2_97)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2665) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (9) and (2008) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2668) aNaturalNumber0(xp) = all_67_2_97
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7362) all_72_3_102 = all_67_2_97
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1243,7362) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1829) all_67_2_97 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1829,7362) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1243) all_72_3_102 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1829) and (2668) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (9) aNaturalNumber0(xp) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (421), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5022)  ~ (aNaturalNumber0(all_0_7_7) = all_57_2_90)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (5022) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1295) and (2129) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (5025) aNaturalNumber0(all_0_7_7) = all_57_2_90
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7386) all_57_2_90 = all_16_0_16
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1789,7386) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1292,7386) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1789) all_57_2_90 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1789) and (5025) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1108), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2446) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2449) aNaturalNumber0(xn) = all_20_0_22
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7378) all_20_0_22 = all_14_2_15
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1828) and (2449) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (411), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1292) and (3485) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1292) all_16_0_16 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1292) and (3488) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (703), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2144)  ~ (aNaturalNumber0(xm) = all_22_2_27)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1788) and (2144) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2147) aNaturalNumber0(xm) = all_22_2_27
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7394) all_72_1_100 = all_22_2_27
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1244,7394) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1788) all_22_2_27 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1788) and (2147) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (564), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1281) and (2039) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7415) all_72_3_102 = all_12_0_10
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1243,7415) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1281) all_12_0_10 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1281,7415) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1243) all_72_3_102 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1281) and (2042) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (582), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2112) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7407) all_82_2_109 = all_57_3_91
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1830,7407) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2199) all_57_3_91 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (2199,7407) yields a new equation:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1830) all_82_2_109 = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1830) and (2115) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1002), into two cases.
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (848) and (2268) follows:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.95/172.82  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2271) aNaturalNumber0(xn) = all_16_1_17
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7427) all_57_1_89 = all_16_1_17
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (980,7427) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (848) all_16_1_17 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (848) and (2271) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (314), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2426)  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (1831) and (2426) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1831) aNaturalNumber0(all_0_2_2) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1830) all_82_2_109 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (418), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2128)  ~ (aNaturalNumber0(all_0_7_7) = all_20_0_22)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1828) and (2128) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1295) and (2129) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2131) aNaturalNumber0(all_0_7_7) = all_20_0_22
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7442) all_20_0_22 = all_16_0_16
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1828,7442) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1292) all_16_0_16 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1292,7442) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1828) all_20_0_22 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1828) and (2131) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (521), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2171) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7434) all_82_3_110 = all_20_0_22
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1247,7434) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1828) all_20_0_22 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1828,7434) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1247) all_82_3_110 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1828) and (2174) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (419), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4226)  ~ (aNaturalNumber0(all_0_7_7) = all_72_2_101)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1791) and (4226) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1295) and (2129) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (4229) aNaturalNumber0(all_0_7_7) = all_72_2_101
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7458) all_72_2_101 = all_16_0_16
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1791,7458) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1292) all_16_0_16 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1292,7458) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1791) all_72_2_101 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1791) and (4229) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1140), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2374)  ~ (aNaturalNumber0(xn) = all_12_0_10)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (2374) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (91) and (1934) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2377) aNaturalNumber0(xn) = all_12_0_10
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7450) all_12_0_10 = all_12_2_12
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1281,7450) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1223) all_12_2_12 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1223,7450) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1281) all_12_0_10 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1281) and (2377) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (91) aNaturalNumber0(xn) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (413), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7470)  ~ (aNaturalNumber0(sz10) = all_16_0_16)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1292) and (7470) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1994)  ~ (aNaturalNumber0(sz10) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (61) and (1994) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7473) aNaturalNumber0(sz10) = all_16_0_16
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1292) all_16_0_16 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (853), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (4124) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7466) all_67_2_97 = all_16_1_17
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1829,7466) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (848) all_16_1_17 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (848,7466) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1829) all_67_2_97 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1829) and (4127) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (972), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2522)  ~ (aNaturalNumber0(xn) = all_39_7_73)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1236) and (2522) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2525) aNaturalNumber0(xn) = all_39_7_73
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7486) all_62_1_93 = all_39_7_73
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1240,7486) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1236) all_39_7_73 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (1236,7486) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1240) all_62_1_93 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1236) and (2525) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (910), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2151) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (91) and (1934) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7479) all_82_1_108 = all_82_2_109
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1249,7479) yields a new equation:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1830) all_82_2_109 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1830) and (2154) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (91) aNaturalNumber0(xn) = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (412), into two cases.
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2984)  ~ (aNaturalNumber0(xn) = all_16_0_16)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1292) and (2984) follows:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (91) and (1934) yields:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2987) aNaturalNumber0(xn) = all_16_0_16
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.83  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1292) and (2987) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (91) aNaturalNumber0(xn) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (454), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2558)  ~ (aNaturalNumber0(all_0_9_9) = all_57_2_90)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1789) and (2558) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2090)  ~ (aNaturalNumber0(all_0_9_9) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (1284) and (2090) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2561) aNaturalNumber0(all_0_9_9) = all_57_2_90
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7494) all_57_2_90 = all_26_2_33
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1789,7494) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1283) all_26_2_33 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (830), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7510)  ~ (aNaturalNumber0(sz00) = all_18_1_20)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1227) and (7510) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (26) and (2070) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7513) aNaturalNumber0(sz00) = all_18_1_20
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1227) all_18_1_20 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1227) and (7513) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (26) aNaturalNumber0(sz00) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (718), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2298)  ~ (aNaturalNumber0(xm) = all_20_0_22)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2298) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (12) and (1940) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2301) aNaturalNumber0(xm) = all_20_0_22
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7506) all_67_1_96 = all_20_0_22
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1242,7506) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1828) all_20_0_22 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1828,7506) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1242) all_67_1_96 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1828) and (2301) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (12) aNaturalNumber0(xm) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (464), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2210)  ~ (aNaturalNumber0(xn) = all_24_2_30)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2210) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2213) aNaturalNumber0(xn) = all_24_2_30
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1282) all_24_2_30 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1282) and (2213) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (774), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (4124) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7520) all_67_2_97 = all_37_3_64
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1829,7520) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1233) all_37_3_64 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1233,7520) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1829) all_67_2_97 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1829) and (4127) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (428), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1985)  ~ (aNaturalNumber0(xn) = all_24_0_28)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (1985) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (91) and (1934) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1988) aNaturalNumber0(xn) = all_24_0_28
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1350) and (1988) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (91) aNaturalNumber0(xn) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (604), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2031)  ~ (aNaturalNumber0(xp) = all_20_2_24)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1787) and (2031) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2034) aNaturalNumber0(xp) = all_20_2_24
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7534) all_52_1_86 = all_20_2_24
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1238,7534) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1787) all_20_2_24 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1787) and (2034) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (393), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2883)  ~ (aNaturalNumber0(all_0_7_7) = all_20_2_24)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1787) and (2883) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (1295) and (2129) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2886) aNaturalNumber0(all_0_7_7) = all_20_2_24
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7555) all_77_2_105 = all_20_2_24
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1294,7555) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1787) all_20_2_24 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1787,7555) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1294) all_77_2_105 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1787) and (2886) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (597), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2112)  ~ (aNaturalNumber0(xp) = all_82_2_109)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (2112) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2115) aNaturalNumber0(xp) = all_82_2_109
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7547) all_82_2_109 = all_52_1_86
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1830,7547) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1238) all_52_1_86 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (1238,7547) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1830) all_82_2_109 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1830) and (2115) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (563), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2475)  ~ (aNaturalNumber0(xp) = all_24_2_30)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2475) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2478) aNaturalNumber0(xp) = all_24_2_30
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7569) all_72_3_102 = all_24_2_30
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1243,7569) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1282) all_24_2_30 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1282,7569) yields a new equation:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1243) all_72_3_102 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1282) and (2478) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (324), into two cases.
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2171)  ~ (aNaturalNumber0(xp) = all_20_0_22)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2171) follows:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (9) and (2008) yields:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2174) aNaturalNumber0(xp) = all_20_0_22
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1828) all_20_0_22 = 0
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.84  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1828) and (2174) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (9) aNaturalNumber0(xp) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (845), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1969)  ~ (aNaturalNumber0(xm) = all_12_0_10)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (1969) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1972) aNaturalNumber0(xm) = all_12_0_10
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7585) all_18_1_20 = all_12_0_10
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1227,7585) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1281) all_12_0_10 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1281,7585) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1227) all_18_1_20 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1281) and (1972) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (983), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2151)  ~ (aNaturalNumber0(xn) = all_82_2_109)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2151) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (91) and (1934) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2154) aNaturalNumber0(xn) = all_82_2_109
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7577) all_82_2_109 = all_57_1_89
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (1830,7577) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (980) all_57_1_89 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Combining equations (980,7577) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1830) all_82_2_109 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1830) and (2154) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (91) aNaturalNumber0(xn) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (329), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2426)  ~ (aNaturalNumber0(all_0_2_2) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (1831) and (2426) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1831) aNaturalNumber0(all_0_2_2) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1828) all_20_0_22 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (886), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3035)  ~ (aNaturalNumber0(xm) = all_52_2_87)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1674) and (3035) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3038) aNaturalNumber0(xm) = all_52_2_87
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7593) all_52_2_87 = all_14_1_14
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1674,7593) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1218) all_14_1_14 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1218,7593) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1674) all_52_2_87 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1674) and (3038) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (328), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7609)  ~ (aNaturalNumber0(sz00) = all_20_0_22)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1828) and (7609) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2070)  ~ (aNaturalNumber0(sz00) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (26) and (2070) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7612) aNaturalNumber0(sz00) = all_20_0_22
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1828) all_20_0_22 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (796), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4124)  ~ (aNaturalNumber0(xm) = all_67_2_97)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (4124) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (12) and (1940) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (4127) aNaturalNumber0(xm) = all_67_2_97
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7605) all_67_2_97 = all_22_1_26
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1829,7605) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1229) all_22_1_26 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1229,7605) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1829) all_67_2_97 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1829) and (4127) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (12) aNaturalNumber0(xm) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (611), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2039)  ~ (aNaturalNumber0(xp) = all_12_0_10)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1281) and (2039) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (9) and (2008) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2042) aNaturalNumber0(xp) = all_12_0_10
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7625) all_52_1_86 = all_12_0_10
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1238,7625) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1281) all_12_0_10 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1281,7625) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1238) all_52_1_86 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1281) and (2042) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (9) aNaturalNumber0(xp) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (572), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1788) and (2105) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7618) all_67_3_98 = all_22_2_27
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1241,7618) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1788) all_22_2_27 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1788) and (2108) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (608), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2899)  ~ (aNaturalNumber0(xp) = all_24_0_28)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (2899) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (9) and (2008) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2902) aNaturalNumber0(xp) = all_24_0_28
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7641) all_52_1_86 = all_24_0_28
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1238,7641) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1350) all_24_0_28 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1350,7641) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1238) all_52_1_86 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1350) and (2902) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (9) aNaturalNumber0(xp) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (823), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2136) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (12) and (1940) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2139) aNaturalNumber0(xm) = all_24_0_28
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7633) all_24_0_28 = all_20_1_23
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1350,7633) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1228) all_20_1_23 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1228,7633) yields a new equation:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1350) all_24_0_28 = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1350) and (2139) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (12) aNaturalNumber0(xm) = 0
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (607), into two cases.
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2023)  ~ (aNaturalNumber0(xp) = all_16_0_16)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1292) and (2023) follows:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (9) and (2008) yields:
% 223.95/172.85  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2026) aNaturalNumber0(xp) = all_16_0_16
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7657) all_52_1_86 = all_16_0_16
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1238,7657) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1292) all_16_0_16 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Combining equations (1292,7657) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1238) all_52_1_86 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1292) and (2026) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (9) aNaturalNumber0(xp) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (622), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1293) and (2159) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (9) and (2008) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7649) all_47_2_83 = all_47_3_84
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1293,7649) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2191) all_47_3_84 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (2191,7649) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1293) all_47_2_83 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1293) and (2162) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (9) aNaturalNumber0(xp) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (606), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1293) and (2159) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (9) and (2008) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (2162) aNaturalNumber0(xp) = all_47_2_83
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7671) all_52_1_86 = all_47_2_83
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1238,7671) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1293) all_47_2_83 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1293) and (2162) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (9) aNaturalNumber0(xp) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (332), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2642)  ~ (aNaturalNumber0(xp) = all_72_2_101)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1791) and (2642) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2645) aNaturalNumber0(xp) = all_72_2_101
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1791) all_72_2_101 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1791) and (2645) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (605), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (3339) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (9) and (2008) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7686) all_77_2_105 = all_52_1_86
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1294,7686) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1238) all_52_1_86 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1238,7686) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1294) all_77_2_105 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1294) and (3342) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (9) aNaturalNumber0(xp) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (905), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2382)  ~ (aNaturalNumber0(xm) = all_24_2_30)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (2382) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (2385) aNaturalNumber0(xm) = all_24_2_30
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7678) all_24_2_30 = all_12_1_11
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1282,7678) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1221) all_12_1_11 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Combining equations (1221,7678) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1282) all_24_2_30 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1282) and (2385) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1093), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2334)  ~ (aNaturalNumber0(xn) = all_67_1_96)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (2334) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (91) and (1934) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2337) aNaturalNumber0(xn) = all_67_1_96
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7700) all_67_1_96 = all_16_2_18
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1242,7700) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1225) all_16_2_18 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1225,7700) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1242) all_67_1_96 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1242) and (2337) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (91) aNaturalNumber0(xn) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (360), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (2105) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (9) and (2008) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2108) aNaturalNumber0(xp) = all_22_2_27
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1788) all_22_2_27 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1788) and (2108) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (9) aNaturalNumber0(xp) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (841), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1292) and (3485) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (12) and (1940) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (3488) aNaturalNumber0(xm) = all_16_0_16
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7716) all_18_1_20 = all_16_0_16
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Combining equations (7716,1227) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2760) all_16_0_16 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Simplifying 2760 yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1292) all_16_0_16 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (1292) and (3488) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (12) aNaturalNumber0(xm) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (899), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2366)  ~ (aNaturalNumber0(xm) = all_20_2_24)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1787) and (2366) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (2369) aNaturalNumber0(xm) = all_20_2_24
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7708) all_20_2_24 = all_12_1_11
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (7708,1787) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3284) all_12_1_11 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Simplifying 3284 yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1221) all_12_1_11 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1787) and (2369) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (416), into two cases.
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3255)  ~ (aNaturalNumber0(all_0_7_7) = all_82_2_109)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (3255) follows:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (1295) and (2129) yields:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (3258) aNaturalNumber0(all_0_7_7) = all_82_2_109
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7731) all_82_2_109 = all_16_0_16
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1830,7731) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1292) all_16_0_16 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Combining equations (1292,7731) yields a new equation:
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1830) all_82_2_109 = 0
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.86  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1830) and (3258) follows:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1295) aNaturalNumber0(all_0_7_7) = 0
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (527), into two cases.
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1294) and (3339) follows:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (9) and (2008) yields:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (3342) aNaturalNumber0(xp) = all_77_2_105
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7724) all_82_3_110 = all_77_2_105
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1247,7724) yields a new equation:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1294) all_77_2_105 = 0
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1294) and (3342) follows:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (9) aNaturalNumber0(xp) = 0
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (861), into two cases.
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2962) follows:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 223.95/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2965) aNaturalNumber0(xm) = all_47_2_83
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7746) all_47_2_83 = all_16_1_17
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1293,7746) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (848) all_16_1_17 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (848,7746) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1293) all_47_2_83 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1293) and (2965) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (12) aNaturalNumber0(xm) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (559), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2159)  ~ (aNaturalNumber0(xp) = all_47_2_83)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2159) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (9) and (2008) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (2162) aNaturalNumber0(xp) = all_47_2_83
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7739) all_72_3_102 = all_47_2_83
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1243,7739) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1293) all_47_2_83 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1293) and (2162) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (9) aNaturalNumber0(xp) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (954), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2081)  ~ (aNaturalNumber0(xn) = all_12_1_11)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1221) and (2081) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (91) and (1934) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2084) aNaturalNumber0(xn) = all_12_1_11
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7762) all_77_1_104 = all_12_1_11
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1246,7762) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1221) all_12_1_11 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1221) and (2084) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (91) aNaturalNumber0(xn) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1021), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2490)  ~ (aNaturalNumber0(xn) = all_47_1_82)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1237) and (2490) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (91) and (1934) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (2493) aNaturalNumber0(xn) = all_47_1_82
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7754) all_47_1_82 = all_39_8_74
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1237,7754) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1179) all_39_8_74 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1179,7754) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1237) all_47_1_82 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1237) and (2493) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (91) aNaturalNumber0(xn) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (400), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2129)  ~ (aNaturalNumber0(all_0_7_7) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (1295) and (2129) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1295) aNaturalNumber0(all_0_7_7) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1293) all_47_2_83 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (960), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2446)  ~ (aNaturalNumber0(xn) = all_20_0_22)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1828) and (2446) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Using (91) and (1934) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (2449) aNaturalNumber0(xn) = all_20_0_22
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7769) all_62_1_93 = all_20_0_22
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Combining equations (1240,7769) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1828) all_20_0_22 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| From (1828) and (2449) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (91) aNaturalNumber0(xn) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (902), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1292) and (3485) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Using (12) and (1940) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (3488) aNaturalNumber0(xm) = all_16_0_16
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7789) all_16_0_16 = all_12_1_11
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1292,7789) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1221) all_12_1_11 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (1221,7789) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (1292) all_16_0_16 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| From (1292) and (3488) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (12) aNaturalNumber0(xm) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (619), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2105)  ~ (aNaturalNumber0(xp) = all_22_2_27)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2105) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Using (9) and (2008) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (2108) aNaturalNumber0(xp) = all_22_2_27
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (7781) all_47_3_84 = all_22_2_27
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Combining equations (7781,2191) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5091) all_22_2_27 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Simplifying 5091 yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (1788) all_22_2_27 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| From (1788) and (2108) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (9) aNaturalNumber0(xp) = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (356), into two cases.
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5480)  ~ (aNaturalNumber0(all_0_3_3) = all_67_2_97)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5480) follows:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Using (1775) and (1780) yields:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1311) $false
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (5483) aNaturalNumber0(all_0_3_3) = all_67_2_97
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (7795) all_67_2_97 = all_57_2_90
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1829,7795) yields a new equation:
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1789) all_57_2_90 = 0
% 224.06/172.87  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Combining equations (1789,7795) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1829) all_67_2_97 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| From (1829) and (5483) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (1775) aNaturalNumber0(all_0_3_3) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												+-Applying beta-rule and splitting (883), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3028)  ~ (aNaturalNumber0(xm) = all_26_2_33)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (3028) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| Using (12) and (1940) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (3031) aNaturalNumber0(xm) = all_26_2_33
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (7811) all_26_2_33 = all_14_1_14
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| From (1283) and (3031) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (12) aNaturalNumber0(xm) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													+-Applying beta-rule and splitting (871), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2097)  ~ (aNaturalNumber0(xm) = all_82_2_109)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (2097) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Using (12) and (1940) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (2100) aNaturalNumber0(xm) = all_82_2_109
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													| (7803) all_82_2_109 = all_14_1_14
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																													|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1830,7803) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1218) all_14_1_14 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| Combining equations (1218,7803) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (1830) all_82_2_109 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| From (1830) and (2100) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (12) aNaturalNumber0(xm) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														+-Applying beta-rule and splitting (882), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2136)  ~ (aNaturalNumber0(xm) = all_24_0_28)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2136) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| Using (12) and (1940) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (2139) aNaturalNumber0(xm) = all_24_0_28
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														| (7823) all_24_0_28 = all_14_1_14
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																														|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| From (1350) and (2139) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (12) aNaturalNumber0(xm) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															+-Applying beta-rule and splitting (1150), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2268)  ~ (aNaturalNumber0(xn) = all_16_1_17)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (848) and (2268) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| Using (91) and (1934) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (2271) aNaturalNumber0(xn) = all_16_1_17
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															| (7817) all_16_1_17 = all_12_2_12
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																															|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| From (848) and (2271) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (91) aNaturalNumber0(xn) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																+-Applying beta-rule and splitting (881), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3485)  ~ (aNaturalNumber0(xm) = all_16_0_16)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3485) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Using (12) and (1940) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (3488) aNaturalNumber0(xm) = all_16_0_16
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																| (7829) all_16_0_16 = all_14_1_14
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1292,7829) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1218) all_14_1_14 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| Combining equations (1218,7829) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (1292) all_16_0_16 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| From (1292) and (3488) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (12) aNaturalNumber0(xm) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	+-Applying beta-rule and splitting (880), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2962)  ~ (aNaturalNumber0(xm) = all_47_2_83)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2962) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| Using (12) and (1940) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (2965) aNaturalNumber0(xm) = all_47_2_83
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	| (7843) all_47_2_83 = all_14_1_14
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																	|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| From (1293) and (2965) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (12) aNaturalNumber0(xm) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1123), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2055)  ~ (aNaturalNumber0(xn) = all_20_1_23)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1228) and (2055) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Using (91) and (1934) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (2058) aNaturalNumber0(xn) = all_20_1_23
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		| (7837) all_20_1_23 = all_14_2_15
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1228,7837) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1200) all_14_2_15 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| Combining equations (1200,7837) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (1228) all_20_1_23 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| From (1228) and (2058) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (91) aNaturalNumber0(xn) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			+-Applying beta-rule and splitting (879), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2275)  ~ (aNaturalNumber0(xm) = all_77_2_105)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| From (1294) and (2275) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1940)  ~ (aNaturalNumber0(xm) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Using (12) and (1940) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (2278) aNaturalNumber0(xm) = all_77_2_105
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			| (7849) all_77_2_105 = all_14_1_14
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																			|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1294,7849) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1218) all_14_1_14 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| Combining equations (1218,7849) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1294) all_77_2_105 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1109), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1953)  ~ (aNaturalNumber0(xn) = all_77_2_105)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| From (1294) and (1953) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1934)  ~ (aNaturalNumber0(xn) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Using (91) and (1934) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (1956) aNaturalNumber0(xn) = all_77_2_105
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				| (7856) all_77_2_105 = all_14_2_15
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																				|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1294,7856) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1200) all_14_2_15 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| Combining equations (1200,7856) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (1294) all_77_2_105 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					+-Applying beta-rule and splitting (367), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2498)  ~ (aNaturalNumber0(all_0_3_3) = all_20_0_22)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2498) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Using (1775) and (1780) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1311) $false
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|-Branch two:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (2501) aNaturalNumber0(all_0_3_3) = all_20_0_22
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					| (7863) all_22_2_27 = all_20_0_22
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																					|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| Combining equations (1788,7863) yields a new equation:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1828) all_20_0_22 = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| From (1828) and (2501) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (1775) aNaturalNumber0(all_0_3_3) = 0
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						+-Applying beta-rule and splitting (574), into two cases.
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch one:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3339)  ~ (aNaturalNumber0(xp) = all_77_2_105)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3339) follows:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (2008)  ~ (aNaturalNumber0(xp) = 0)
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Using (9) and (2008) yields:
% 224.06/172.88  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1311) $false
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|-Branch two:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (3342) aNaturalNumber0(xp) = all_77_2_105
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						| (7870) all_77_2_105 = all_67_3_98
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																						|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1294,7870) yields a new equation:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1241) all_67_3_98 = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| Combining equations (1241,7870) yields a new equation:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1294) all_77_2_105 = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| From (1294) and (3342) follows:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (9) aNaturalNumber0(xp) = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							+-Applying beta-rule and splitting (303), into two cases.
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch one:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7874)  ~ (doDivides0(xp, all_0_3_3) = all_39_3_69)
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1313) and (7874) follows:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7875)  ~ (doDivides0(xp, all_0_3_3) = 0)
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Using (70) and (7875) yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1311) $false
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|-Branch two:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (7877) doDivides0(xp, all_0_3_3) = all_39_3_69
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							| (1313) all_39_3_69 = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																							|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| From (1313) and (7877) follows:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (70) doDivides0(xp, all_0_3_3) = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating formula (20) with all_642_0_217, all_0_3_3, xp and discharging atoms sdtlseqdt0(xp, all_0_3_3) = all_642_0_217, yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7880) all_642_0_217 = 0 | all_0_3_3 = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating formula (34) with all_226_1_142, xp, xn and discharging atoms sdtpldt0(xn, xp) = all_226_1_142, yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7883)  ? [v0] :  ? [v1] :  ? [v2] : (aNaturalNumber0(all_226_1_142) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Instantiating (7883) with all_6293_0_609, all_6293_1_610, all_6293_2_611 yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (13898) aNaturalNumber0(all_226_1_142) = all_6293_0_609 & aNaturalNumber0(xp) = all_6293_1_610 & aNaturalNumber0(xn) = all_6293_2_611 & ( ~ (all_6293_1_610 = 0) |  ~ (all_6293_2_611 = 0) | all_6293_0_609 = 0)
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| Applying alpha-rule on (13898) yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (13899) aNaturalNumber0(all_226_1_142) = all_6293_0_609
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (13900) aNaturalNumber0(xp) = all_6293_1_610
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (13901) aNaturalNumber0(xn) = all_6293_2_611
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (13902)  ~ (all_6293_1_610 = 0) |  ~ (all_6293_2_611 = 0) | all_6293_0_609 = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								+-Applying beta-rule and splitting (7880), into two cases.
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch one:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1901) all_0_3_3 = sz00
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| Equations (1901) can reduce 1898 to:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (197) $false
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|-Branch two:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (1898)  ~ (all_0_3_3 = sz00)
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								| (7892) all_642_0_217 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																								|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									+-Applying beta-rule and splitting (7892), into two cases.
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch one:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7893) all_642_0_217 = 0
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Equations (7893) can reduce 1849 to:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (197) $false
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|-Branch two:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (1849)  ~ (all_642_0_217 = 0)
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									| (7896)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating (7896) with all_6321_0_618, all_6321_1_619, all_6321_2_620 yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13911) doDivides0(xp, all_0_3_3) = all_6321_0_618 & aNaturalNumber0(all_0_3_3) = all_6321_1_619 & aNaturalNumber0(xp) = all_6321_2_620 & ( ~ (all_6321_0_618 = 0) |  ~ (all_6321_1_619 = 0) |  ~ (all_6321_2_620 = 0))
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Applying alpha-rule on (13911) yields:
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13912) doDivides0(xp, all_0_3_3) = all_6321_0_618
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13913) aNaturalNumber0(all_0_3_3) = all_6321_1_619
% 224.06/172.89  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13914) aNaturalNumber0(xp) = all_6321_2_620
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13915)  ~ (all_6321_0_618 = 0) |  ~ (all_6321_1_619 = 0) |  ~ (all_6321_2_620 = 0)
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (79) with xp, all_0_3_3, all_6321_0_618, 0 and discharging atoms doDivides0(xp, all_0_3_3) = all_6321_0_618, doDivides0(xp, all_0_3_3) = 0, yields:
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13916) all_6321_0_618 = 0
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with all_0_3_3, all_6321_1_619, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_6321_1_619, aNaturalNumber0(all_0_3_3) = 0, yields:
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13917) all_6321_1_619 = 0
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with xp, all_6321_2_620, 0 and discharging atoms aNaturalNumber0(xp) = all_6321_2_620, aNaturalNumber0(xp) = 0, yields:
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13918) all_6321_2_620 = 0
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Instantiating formula (28) with xp, all_6293_1_610, all_6321_2_620 and discharging atoms aNaturalNumber0(xp) = all_6321_2_620, aNaturalNumber0(xp) = all_6293_1_610, yields:
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13919) all_6321_2_620 = all_6293_1_610
% 224.06/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (13918,13919) yields a new equation:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13920) all_6293_1_610 = 0
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| Combining equations (13920,13919) yields a new equation:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13918) all_6321_2_620 = 0
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										+-Applying beta-rule and splitting (13915), into two cases.
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch one:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13922)  ~ (all_6321_0_618 = 0)
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| Equations (13916) can reduce 13922 to:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (197) $false
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|-Branch two:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13916) all_6321_0_618 = 0
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										| (13925)  ~ (all_6321_1_619 = 0) |  ~ (all_6321_2_620 = 0)
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																										|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											+-Applying beta-rule and splitting (13925), into two cases.
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch one:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (13926)  ~ (all_6321_1_619 = 0)
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Equations (13917) can reduce 13926 to:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (197) $false
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|-Branch two:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (13917) all_6321_1_619 = 0
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											| (13929)  ~ (all_6321_2_620 = 0)
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																											|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| Equations (13918) can reduce 13929 to:
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												| (197) $false
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|
% 224.09/172.90  																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 224.12/172.98  																																																																													|-Branch two:
% 224.12/172.98  																																																																													| (13931) sdtasdt0(sz00, xm) = all_0_2_2
% 224.12/172.98  																																																																													| (13932)  ? [v0] :  ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_2_2 = sz00)))
% 224.12/172.98  																																																																													|
% 224.12/172.98  																																																																														| Instantiating (13932) with all_879_0_645, all_879_1_646 yields:
% 224.12/172.98  																																																																														| (13933) sdtasdt0(xm, sz00) = all_879_0_645 & aNaturalNumber0(xm) = all_879_1_646 & ( ~ (all_879_1_646 = 0) | (all_879_0_645 = sz00 & all_0_2_2 = sz00))
% 224.12/172.98  																																																																														|
% 224.12/172.98  																																																																														| Applying alpha-rule on (13933) yields:
% 224.12/172.98  																																																																														| (13934) sdtasdt0(xm, sz00) = all_879_0_645
% 224.12/172.98  																																																																														| (13935) aNaturalNumber0(xm) = all_879_1_646
% 224.12/172.98  																																																																														| (13936)  ~ (all_879_1_646 = 0) | (all_879_0_645 = sz00 & all_0_2_2 = sz00)
% 224.12/172.98  																																																																														|
% 224.12/172.98  																																																																														| Instantiating formula (28) with xm, all_879_1_646, 0 and discharging atoms aNaturalNumber0(xm) = all_879_1_646, aNaturalNumber0(xm) = 0, yields:
% 224.12/172.98  																																																																														| (13937) all_879_1_646 = 0
% 224.12/172.98  																																																																														|
% 224.12/172.98  																																																																														| From (13937) and (13935) follows:
% 224.12/172.99  																																																																														| (12) aNaturalNumber0(xm) = 0
% 224.12/172.99  																																																																														|
% 224.12/172.99  																																																																														+-Applying beta-rule and splitting (13936), into two cases.
% 224.12/172.99  																																																																														|-Branch one:
% 224.12/172.99  																																																																														| (13939)  ~ (all_879_1_646 = 0)
% 224.12/172.99  																																																																														|
% 224.12/172.99  																																																																															| Equations (13937) can reduce 13939 to:
% 224.12/172.99  																																																																															| (197) $false
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															|-The branch is then unsatisfiable
% 224.12/172.99  																																																																														|-Branch two:
% 224.12/172.99  																																																																														| (13937) all_879_1_646 = 0
% 224.12/172.99  																																																																														| (13942) all_879_0_645 = sz00 & all_0_2_2 = sz00
% 224.12/172.99  																																																																														|
% 224.12/172.99  																																																																															| Applying alpha-rule on (13942) yields:
% 224.12/172.99  																																																																															| (13943) all_879_0_645 = sz00
% 224.12/172.99  																																																																															| (13944) all_0_2_2 = sz00
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															| Equations (13944) can reduce 1893 to:
% 224.12/172.99  																																																																															| (13945)  ~ (xm = sz00)
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															| Simplifying 13945 yields:
% 224.12/172.99  																																																																															| (1845)  ~ (xm = sz00)
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															| From (13944) and (45) follows:
% 224.12/172.99  																																																																															| (13947) sdtasdt0(all_0_3_3, xm) = sz00
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															| From (13944) and (1819) follows:
% 224.12/172.99  																																																																															| (13948) sdtasdt0(xr, sz00) = all_0_7_7
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															| From (13944) and (1807) follows:
% 224.12/172.99  																																																																															| (13949) sdtasdt0(xm, all_0_3_3) = sz00
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																															+-Applying beta-rule and splitting (117), into two cases.
% 224.12/172.99  																																																																															|-Branch one:
% 224.12/172.99  																																																																															| (13950)  ~ (sdtasdt0(all_0_3_3, xm) = sz00)
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																																| Using (13947) and (13950) yields:
% 224.12/172.99  																																																																																| (1311) $false
% 224.12/172.99  																																																																																|
% 224.12/172.99  																																																																																|-The branch is then unsatisfiable
% 224.12/172.99  																																																																															|-Branch two:
% 224.12/172.99  																																																																															| (13947) sdtasdt0(all_0_3_3, xm) = sz00
% 224.12/172.99  																																																																															| (13953) all_0_3_3 = sz00 | xm = sz00 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/172.99  																																																																															|
% 224.12/172.99  																																																																																+-Applying beta-rule and splitting (13953), into two cases.
% 224.12/172.99  																																																																																|-Branch one:
% 224.12/172.99  																																																																																| (1901) all_0_3_3 = sz00
% 224.12/172.99  																																																																																|
% 224.12/172.99  																																																																																	| Combining equations (1901,1773) yields a new equation:
% 224.12/172.99  																																																																																	| (1899) all_34_2_54 = sz00
% 224.12/172.99  																																																																																	|
% 224.12/172.99  																																																																																	+-Applying beta-rule and splitting (1545), into two cases.
% 224.12/172.99  																																																																																	|-Branch one:
% 224.12/172.99  																																																																																	| (13956)  ~ (sdtasdt0(xr, all_34_2_54) = all_244_0_180)
% 224.12/172.99  																																																																																	|
% 224.12/172.99  																																																																																		| From (1899)(1734) and (13956) follows:
% 224.12/172.99  																																																																																		| (13957)  ~ (sdtasdt0(xr, sz00) = all_0_7_7)
% 224.12/172.99  																																																																																		|
% 224.12/172.99  																																																																																		| Using (13948) and (13957) yields:
% 224.12/172.99  																																																																																		| (1311) $false
% 224.12/172.99  																																																																																		|
% 224.12/172.99  																																																																																		|-The branch is then unsatisfiable
% 224.12/172.99  																																																																																	|-Branch two:
% 224.12/172.99  																																																																																	| (13959) sdtasdt0(xr, all_34_2_54) = all_244_0_180
% 224.12/173.00  																																																																																	| (13960) all_244_0_180 = xn
% 224.12/173.00  																																																																																	|
% 224.12/173.00  																																																																																		| Combining equations (1734,13960) yields a new equation:
% 224.12/173.00  																																																																																		| (13961) all_0_7_7 = xn
% 224.12/173.00  																																																																																		|
% 224.12/173.00  																																																																																		| Simplifying 13961 yields:
% 224.12/173.00  																																																																																		| (13962) all_0_7_7 = xn
% 224.12/173.00  																																																																																		|
% 224.12/173.00  																																																																																		| Equations (13962) can reduce 1764 to:
% 224.12/173.00  																																																																																		| (197) $false
% 224.12/173.00  																																																																																		|
% 224.12/173.00  																																																																																		|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																|-Branch two:
% 224.12/173.00  																																																																																| (1898)  ~ (all_0_3_3 = sz00)
% 224.12/173.00  																																																																																| (13965) xm = sz00 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.00  																																																																																|
% 224.12/173.00  																																																																																	+-Applying beta-rule and splitting (1380), into two cases.
% 224.12/173.00  																																																																																	|-Branch one:
% 224.12/173.00  																																																																																	| (13966)  ~ (sdtasdt0(xm, all_0_3_3) = sz00)
% 224.12/173.00  																																																																																	|
% 224.12/173.00  																																																																																		| Using (13949) and (13966) yields:
% 224.12/173.00  																																																																																		| (1311) $false
% 224.12/173.00  																																																																																		|
% 224.12/173.00  																																																																																		|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																	|-Branch two:
% 224.12/173.00  																																																																																	| (13949) sdtasdt0(xm, all_0_3_3) = sz00
% 224.12/173.00  																																																																																	| (13969) all_0_3_3 = sz00 | xm = sz00 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.00  																																																																																	|
% 224.12/173.00  																																																																																		+-Applying beta-rule and splitting (1404), into two cases.
% 224.12/173.00  																																																																																		|-Branch one:
% 224.12/173.00  																																																																																		| (1899) all_34_2_54 = sz00
% 224.12/173.00  																																																																																		|
% 224.12/173.00  																																																																																			| Combining equations (1773,1899) yields a new equation:
% 224.12/173.00  																																																																																			| (1900) all_0_3_3 = sz00
% 224.12/173.00  																																																																																			|
% 224.12/173.00  																																																																																			| Simplifying 1900 yields:
% 224.12/173.00  																																																																																			| (1901) all_0_3_3 = sz00
% 224.12/173.00  																																																																																			|
% 224.12/173.00  																																																																																			| Equations (1901) can reduce 1898 to:
% 224.12/173.00  																																																																																			| (197) $false
% 224.12/173.00  																																																																																			|
% 224.12/173.00  																																																																																			|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																		|-Branch two:
% 224.12/173.00  																																																																																		| (1903)  ~ (all_34_2_54 = sz00)
% 224.12/173.00  																																																																																		| (1904) all_34_2_54 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_34_2_54) = 0 & aNaturalNumber0(v0) = 0)
% 224.12/173.00  																																																																																		|
% 224.12/173.00  																																																																																			| Equations (1773) can reduce 1903 to:
% 224.12/173.00  																																																																																			| (1898)  ~ (all_0_3_3 = sz00)
% 224.12/173.00  																																																																																			|
% 224.12/173.00  																																																																																			+-Applying beta-rule and splitting (13969), into two cases.
% 224.12/173.00  																																																																																			|-Branch one:
% 224.12/173.00  																																																																																			| (1901) all_0_3_3 = sz00
% 224.12/173.00  																																																																																			|
% 224.12/173.00  																																																																																				| Equations (1901) can reduce 1898 to:
% 224.12/173.00  																																																																																				| (197) $false
% 224.12/173.00  																																																																																				|
% 224.12/173.00  																																																																																				|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																			|-Branch two:
% 224.12/173.00  																																																																																			| (1898)  ~ (all_0_3_3 = sz00)
% 224.12/173.00  																																																																																			| (13980) xm = sz00 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.00  																																																																																			|
% 224.12/173.00  																																																																																				+-Applying beta-rule and splitting (1370), into two cases.
% 224.12/173.00  																																																																																				|-Branch one:
% 224.12/173.00  																																																																																				| (1901) all_0_3_3 = sz00
% 224.12/173.00  																																																																																				|
% 224.12/173.00  																																																																																					| Equations (1901) can reduce 1898 to:
% 224.12/173.00  																																																																																					| (197) $false
% 224.12/173.00  																																																																																					|
% 224.12/173.00  																																																																																					|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																				|-Branch two:
% 224.12/173.00  																																																																																				| (1898)  ~ (all_0_3_3 = sz00)
% 224.12/173.00  																																																																																				| (1909) all_62_0_92 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.00  																																																																																				|
% 224.12/173.00  																																																																																					+-Applying beta-rule and splitting (13980), into two cases.
% 224.12/173.00  																																																																																					|-Branch one:
% 224.12/173.00  																																																																																					| (1850) xm = sz00
% 224.12/173.00  																																																																																					|
% 224.12/173.00  																																																																																						| Equations (1850) can reduce 1845 to:
% 224.12/173.00  																																																																																						| (197) $false
% 224.12/173.00  																																																																																						|
% 224.12/173.00  																																																																																						|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																					|-Branch two:
% 224.12/173.00  																																																																																					| (1845)  ~ (xm = sz00)
% 224.12/173.00  																																																																																					| (13988)  ? [v0] :  ? [v1] : (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.00  																																																																																					|
% 224.12/173.00  																																																																																						| Instantiating (13988) with all_919_0_647, all_919_1_648 yields:
% 224.12/173.00  																																																																																						| (13989) aNaturalNumber0(all_0_3_3) = all_919_0_647 & aNaturalNumber0(xm) = all_919_1_648 & ( ~ (all_919_0_647 = 0) |  ~ (all_919_1_648 = 0))
% 224.12/173.00  																																																																																						|
% 224.12/173.00  																																																																																						| Applying alpha-rule on (13989) yields:
% 224.12/173.00  																																																																																						| (13990) aNaturalNumber0(all_0_3_3) = all_919_0_647
% 224.12/173.00  																																																																																						| (13991) aNaturalNumber0(xm) = all_919_1_648
% 224.12/173.00  																																																																																						| (13992)  ~ (all_919_0_647 = 0) |  ~ (all_919_1_648 = 0)
% 224.12/173.00  																																																																																						|
% 224.12/173.00  																																																																																						+-Applying beta-rule and splitting (1406), into two cases.
% 224.12/173.00  																																																																																						|-Branch one:
% 224.12/173.00  																																																																																						| (1780)  ~ (aNaturalNumber0(all_0_3_3) = 0)
% 224.12/173.00  																																																																																						|
% 224.12/173.00  																																																																																							| Using (1775) and (1780) yields:
% 224.12/173.00  																																																																																							| (1311) $false
% 224.12/173.00  																																																																																							|
% 224.12/173.00  																																																																																							|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																						|-Branch two:
% 224.12/173.00  																																																																																						| (1775) aNaturalNumber0(all_0_3_3) = 0
% 224.12/173.00  																																																																																						| (1913) all_0_3_3 = sz10 | all_0_3_3 = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_0_3_3) = 0 & aNaturalNumber0(v0) = 0)
% 224.12/173.00  																																																																																						|
% 224.12/173.00  																																																																																							+-Applying beta-rule and splitting (1909), into two cases.
% 224.12/173.00  																																																																																							|-Branch one:
% 224.12/173.00  																																																																																							| (1832) all_62_0_92 = 0
% 224.12/173.00  																																																																																							|
% 224.12/173.00  																																																																																								| Equations (1832) can reduce 1802 to:
% 224.12/173.00  																																																																																								| (197) $false
% 224.12/173.00  																																																																																								|
% 224.12/173.00  																																																																																								|-The branch is then unsatisfiable
% 224.12/173.00  																																																																																							|-Branch two:
% 224.12/173.00  																																																																																							| (1802)  ~ (all_62_0_92 = 0)
% 224.12/173.00  																																																																																							| (1917)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xn, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.00  																																																																																							|
% 224.12/173.00  																																																																																								| Instantiating (1917) with all_933_0_650, all_933_1_651, all_933_2_652 yields:
% 224.12/173.00  																																																																																								| (14001) doDivides0(xn, all_0_3_3) = all_933_0_650 & aNaturalNumber0(all_0_3_3) = all_933_1_651 & aNaturalNumber0(xn) = all_933_2_652 & ( ~ (all_933_0_650 = 0) |  ~ (all_933_1_651 = 0) |  ~ (all_933_2_652 = 0))
% 224.12/173.00  																																																																																								|
% 224.12/173.01  																																																																																								| Applying alpha-rule on (14001) yields:
% 224.12/173.01  																																																																																								| (14002) doDivides0(xn, all_0_3_3) = all_933_0_650
% 224.12/173.01  																																																																																								| (14003) aNaturalNumber0(all_0_3_3) = all_933_1_651
% 224.12/173.01  																																																																																								| (14004) aNaturalNumber0(xn) = all_933_2_652
% 224.12/173.01  																																																																																								| (14005)  ~ (all_933_0_650 = 0) |  ~ (all_933_1_651 = 0) |  ~ (all_933_2_652 = 0)
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																								| Instantiating formula (28) with all_0_3_3, all_933_1_651, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_933_1_651, aNaturalNumber0(all_0_3_3) = 0, yields:
% 224.12/173.01  																																																																																								| (14006) all_933_1_651 = 0
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																								| Instantiating formula (28) with all_0_3_3, all_919_0_647, all_933_1_651 and discharging atoms aNaturalNumber0(all_0_3_3) = all_933_1_651, aNaturalNumber0(all_0_3_3) = all_919_0_647, yields:
% 224.12/173.01  																																																																																								| (14007) all_933_1_651 = all_919_0_647
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																								| Instantiating formula (28) with xm, all_919_1_648, 0 and discharging atoms aNaturalNumber0(xm) = all_919_1_648, aNaturalNumber0(xm) = 0, yields:
% 224.12/173.01  																																																																																								| (14008) all_919_1_648 = 0
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																								| Combining equations (14006,14007) yields a new equation:
% 224.12/173.01  																																																																																								| (14009) all_919_0_647 = 0
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																								+-Applying beta-rule and splitting (13992), into two cases.
% 224.12/173.01  																																																																																								|-Branch one:
% 224.12/173.01  																																																																																								| (14010)  ~ (all_919_0_647 = 0)
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																									| Equations (14009) can reduce 14010 to:
% 224.12/173.01  																																																																																									| (197) $false
% 224.12/173.01  																																																																																									|
% 224.12/173.01  																																																																																									|-The branch is then unsatisfiable
% 224.12/173.01  																																																																																								|-Branch two:
% 224.12/173.01  																																																																																								| (14009) all_919_0_647 = 0
% 224.12/173.01  																																																																																								| (14013)  ~ (all_919_1_648 = 0)
% 224.12/173.01  																																																																																								|
% 224.12/173.01  																																																																																									| Equations (14008) can reduce 14013 to:
% 224.12/173.01  																																																																																									| (197) $false
% 224.12/173.01  																																																																																									|
% 224.12/173.01  																																																																																									|-The branch is then unsatisfiable
% 224.12/173.01  																																																																								|-Branch two:
% 224.12/173.01  																																																																								| (14015) sdtasdt0(all_0_3_3, xm) = xm
% 224.12/173.01  																																																																								| (14016) all_72_0_99 = 0 |  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(xm) = v0) | (aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 224.12/173.01  																																																																								|
% 224.12/173.01  																																																																									+-Applying beta-rule and splitting (1383), into two cases.
% 224.12/173.01  																																																																									|-Branch one:
% 224.12/173.01  																																																																									| (1854)  ~ (sdtasdt0(all_0_3_3, xm) = xm)
% 224.12/173.01  																																																																									|
% 224.12/173.01  																																																																										| Using (14015) and (1854) yields:
% 224.12/173.01  																																																																										| (1311) $false
% 224.12/173.01  																																																																										|
% 224.12/173.01  																																																																										|-The branch is then unsatisfiable
% 224.12/173.01  																																																																									|-Branch two:
% 224.12/173.02  																																																																									| (14015) sdtasdt0(all_0_3_3, xm) = xm
% 224.12/173.02  																																																																									| (14020)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (sdtasdt0(all_0_3_3, v3) = v4 & sdtasdt0(xm, xn) = v3 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v4 = all_0_7_7))
% 224.12/173.02  																																																																									|
% 224.12/173.02  																																																																										| Instantiating formula (49) with all_0_3_3, xm, xm, all_0_2_2 and discharging atoms sdtasdt0(all_0_3_3, xm) = all_0_2_2, sdtasdt0(all_0_3_3, xm) = xm, yields:
% 224.12/173.02  																																																																										| (14021) all_0_2_2 = xm
% 224.12/173.02  																																																																										|
% 224.12/173.02  																																																																										| From (14021) and (81) follows:
% 224.12/173.02  																																																																										| (14022) doDivides0(xp, xm) = 0
% 224.12/173.02  																																																																										|
% 224.12/173.02  																																																																										+-Applying beta-rule and splitting (97), into two cases.
% 224.12/173.02  																																																																										|-Branch one:
% 224.12/173.02  																																																																										| (14023)  ~ (doDivides0(xp, xm) = 0)
% 224.12/173.02  																																																																										|
% 224.12/173.02  																																																																											| Using (14022) and (14023) yields:
% 224.12/173.02  																																																																											| (1311) $false
% 224.12/173.02  																																																																											|
% 224.12/173.02  																																																																											|-The branch is then unsatisfiable
% 224.12/173.02  																																																																										|-Branch two:
% 224.12/173.02  																																																																										| (14022) doDivides0(xp, xm) = 0
% 224.12/173.02  																																																																										| (196) all_0_1_1 = 0
% 224.12/173.02  																																																																										|
% 224.12/173.02  																																																																											| Equations (196) can reduce 72 to:
% 224.12/173.02  																																																																											| (197) $false
% 224.12/173.02  																																																																											|
% 224.12/173.02  																																																																											|-The branch is then unsatisfiable
% 224.12/173.02  																																																																						|-Branch two:
% 224.12/173.02  																																																																						| (7893) all_642_0_217 = 0
% 224.12/173.02  																																																																						| (14029)  ~ (all_642_1_218 = 0) |  ~ (all_642_2_219 = 0) |  ~ (all_642_3_220 = 0)
% 224.12/173.02  																																																																						|
% 224.12/173.02  																																																																							+-Applying beta-rule and splitting (14029), into two cases.
% 224.12/173.02  																																																																							|-Branch one:
% 224.12/173.02  																																																																							| (14030)  ~ (all_642_1_218 = 0)
% 224.12/173.02  																																																																							|
% 224.12/173.02  																																																																								| Equations (1842) can reduce 14030 to:
% 224.12/173.02  																																																																								| (197) $false
% 224.12/173.02  																																																																								|
% 224.12/173.02  																																																																								|-The branch is then unsatisfiable
% 224.12/173.02  																																																																							|-Branch two:
% 224.12/173.02  																																																																							| (1842) all_642_1_218 = 0
% 224.12/173.02  																																																																							| (14033)  ~ (all_642_2_219 = 0) |  ~ (all_642_3_220 = 0)
% 224.12/173.02  																																																																							|
% 224.12/173.02  																																																																								+-Applying beta-rule and splitting (14033), into two cases.
% 224.12/173.02  																																																																								|-Branch one:
% 224.12/173.02  																																																																								| (14034)  ~ (all_642_2_219 = 0)
% 224.12/173.02  																																																																								|
% 224.12/173.02  																																																																									| Equations (1843) can reduce 14034 to:
% 224.12/173.02  																																																																									| (197) $false
% 224.12/173.02  																																																																									|
% 224.12/173.02  																																																																									|-The branch is then unsatisfiable
% 224.12/173.02  																																																																								|-Branch two:
% 224.12/173.02  																																																																								| (1843) all_642_2_219 = 0
% 224.12/173.02  																																																																								| (14037)  ~ (all_642_3_220 = 0)
% 224.12/173.02  																																																																								|
% 224.12/173.02  																																																																									| Equations (1844) can reduce 14037 to:
% 224.12/173.02  																																																																									| (197) $false
% 224.12/173.02  																																																																									|
% 224.12/173.02  																																																																									|-The branch is then unsatisfiable
% 224.12/173.02  																																																																	|-Branch two:
% 224.12/173.02  																																																																	| (14039) aNaturalNumber0(all_0_3_3) = all_32_2_48 & aNaturalNumber0(xn) = all_32_1_47 & ( ~ (all_32_1_47 = 0) |  ~ (all_32_2_48 = 0))
% 224.12/173.02  																																																																	|
% 224.12/173.02  																																																																		| Applying alpha-rule on (14039) yields:
% 224.12/173.02  																																																																		| (14040) aNaturalNumber0(all_0_3_3) = all_32_2_48
% 224.12/173.02  																																																																		| (14041) aNaturalNumber0(xn) = all_32_1_47
% 224.12/173.02  																																																																		| (14042)  ~ (all_32_1_47 = 0) |  ~ (all_32_2_48 = 0)
% 224.12/173.02  																																																																		|
% 224.12/173.02  																																																																		+-Applying beta-rule and splitting (1367), into two cases.
% 224.12/173.02  																																																																		|-Branch one:
% 224.12/173.02  																																																																		| (1832) all_62_0_92 = 0
% 224.12/173.02  																																																																		|
% 224.12/173.02  																																																																			| Equations (1832) can reduce 1802 to:
% 224.12/173.02  																																																																			| (197) $false
% 224.12/173.02  																																																																			|
% 224.12/173.02  																																																																			|-The branch is then unsatisfiable
% 224.12/173.02  																																																																		|-Branch two:
% 224.12/173.02  																																																																		| (1802)  ~ (all_62_0_92 = 0)
% 224.12/173.02  																																																																		| (1835)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtlseqdt0(xp, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.12/173.02  																																																																		|
% 224.12/173.02  																																																																			| Instantiating (1835) with all_634_0_663, all_634_1_664, all_634_2_665, all_634_3_666 yields:
% 224.12/173.03  																																																																			| (14047) sdtlseqdt0(xp, all_0_3_3) = all_634_0_663 & aNaturalNumber0(all_0_3_3) = all_634_1_664 & aNaturalNumber0(xp) = all_634_2_665 & aNaturalNumber0(xn) = all_634_3_666 & ( ~ (all_634_0_663 = 0) |  ~ (all_634_1_664 = 0) |  ~ (all_634_2_665 = 0) |  ~ (all_634_3_666 = 0))
% 224.12/173.03  																																																																			|
% 224.12/173.03  																																																																			| Applying alpha-rule on (14047) yields:
% 224.12/173.03  																																																																			| (14048)  ~ (all_634_0_663 = 0) |  ~ (all_634_1_664 = 0) |  ~ (all_634_2_665 = 0) |  ~ (all_634_3_666 = 0)
% 224.12/173.03  																																																																			| (14049) aNaturalNumber0(all_0_3_3) = all_634_1_664
% 224.22/173.03  																																																																			| (14050) aNaturalNumber0(xn) = all_634_3_666
% 224.22/173.03  																																																																			| (14051) aNaturalNumber0(xp) = all_634_2_665
% 224.22/173.03  																																																																			| (14052) sdtlseqdt0(xp, all_0_3_3) = all_634_0_663
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			| Instantiating formula (28) with all_0_3_3, all_634_1_664, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_634_1_664, aNaturalNumber0(all_0_3_3) = 0, yields:
% 224.22/173.03  																																																																			| (14053) all_634_1_664 = 0
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			| Instantiating formula (28) with all_0_3_3, all_32_2_48, all_634_1_664 and discharging atoms aNaturalNumber0(all_0_3_3) = all_634_1_664, aNaturalNumber0(all_0_3_3) = all_32_2_48, yields:
% 224.22/173.03  																																																																			| (14054) all_634_1_664 = all_32_2_48
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			| Instantiating formula (28) with xn, all_634_3_666, 0 and discharging atoms aNaturalNumber0(xn) = all_634_3_666, aNaturalNumber0(xn) = 0, yields:
% 224.22/173.03  																																																																			| (14055) all_634_3_666 = 0
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			| Instantiating formula (28) with xn, all_32_1_47, all_634_3_666 and discharging atoms aNaturalNumber0(xn) = all_634_3_666, aNaturalNumber0(xn) = all_32_1_47, yields:
% 224.22/173.03  																																																																			| (14056) all_634_3_666 = all_32_1_47
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			| Combining equations (14053,14054) yields a new equation:
% 224.22/173.03  																																																																			| (14057) all_32_2_48 = 0
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			| Combining equations (14055,14056) yields a new equation:
% 224.22/173.03  																																																																			| (1811) all_32_1_47 = 0
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																			+-Applying beta-rule and splitting (14042), into two cases.
% 224.22/173.03  																																																																			|-Branch one:
% 224.22/173.03  																																																																			| (14059)  ~ (all_32_1_47 = 0)
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																				| Equations (1811) can reduce 14059 to:
% 224.22/173.03  																																																																				| (197) $false
% 224.22/173.03  																																																																				|
% 224.22/173.03  																																																																				|-The branch is then unsatisfiable
% 224.22/173.03  																																																																			|-Branch two:
% 224.22/173.03  																																																																			| (1811) all_32_1_47 = 0
% 224.22/173.03  																																																																			| (14062)  ~ (all_32_2_48 = 0)
% 224.22/173.03  																																																																			|
% 224.22/173.03  																																																																				| Equations (14057) can reduce 14062 to:
% 224.22/173.03  																																																																				| (197) $false
% 224.22/173.03  																																																																				|
% 224.22/173.03  																																																																				|-The branch is then unsatisfiable
% 224.22/173.03  																																																															|-Branch two:
% 224.22/173.03  																																																															| (1832) all_62_0_92 = 0
% 224.22/173.03  																																																															| (14065)  ~ (all_62_1_93 = 0) |  ~ (all_62_2_94 = 0)
% 224.22/173.03  																																																															|
% 224.22/173.03  																																																																| From (1832) and (230) follows:
% 224.22/173.03  																																																																| (14066) sdtlseqdt0(xn, all_0_3_3) = 0
% 224.22/173.03  																																																																|
% 224.22/173.03  																																																																| Using (14066) and (1797) yields:
% 224.22/173.03  																																																																| (1311) $false
% 224.22/173.03  																																																																|
% 224.22/173.03  																																																																|-The branch is then unsatisfiable
% 224.22/173.04  																																																													|-Branch two:
% 224.22/173.04  																																																													| (14066) sdtlseqdt0(xn, all_0_3_3) = 0
% 224.22/173.04  																																																													| (14069) all_0_3_3 = xn |  ? [v0] :  ? [v1] :  ? [v2] : (sdtlseqdt0(all_0_3_3, xn) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.04  																																																													|
% 224.22/173.04  																																																														+-Applying beta-rule and splitting (1369), into two cases.
% 224.22/173.04  																																																														|-Branch one:
% 224.22/173.04  																																																														| (1797)  ~ (sdtlseqdt0(xn, all_0_3_3) = 0)
% 224.22/173.04  																																																														|
% 224.22/173.04  																																																															| Using (14066) and (1797) yields:
% 224.22/173.04  																																																															| (1311) $false
% 224.22/173.04  																																																															|
% 224.22/173.04  																																																															|-The branch is then unsatisfiable
% 224.22/173.04  																																																														|-Branch two:
% 224.22/173.04  																																																														| (14066) sdtlseqdt0(xn, all_0_3_3) = 0
% 224.22/173.04  																																																														| (14073)  ? [v0] :  ? [v1] :  ? [v2] : ((v2 = all_0_3_3 & v1 = 0 & sdtpldt0(xn, v0) = all_0_3_3 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 224.22/173.04  																																																														|
% 224.22/173.04  																																																															+-Applying beta-rule and splitting (233), into two cases.
% 224.22/173.04  																																																															|-Branch one:
% 224.22/173.04  																																																															| (1802)  ~ (all_62_0_92 = 0)
% 224.22/173.04  																																																															|
% 224.22/173.04  																																																																+-Applying beta-rule and splitting (1367), into two cases.
% 224.22/173.04  																																																																|-Branch one:
% 224.22/173.04  																																																																| (1832) all_62_0_92 = 0
% 224.22/173.04  																																																																|
% 224.22/173.04  																																																																	| Equations (1832) can reduce 1802 to:
% 224.22/173.04  																																																																	| (197) $false
% 224.22/173.04  																																																																	|
% 224.22/173.04  																																																																	|-The branch is then unsatisfiable
% 224.22/173.04  																																																																|-Branch two:
% 224.22/173.04  																																																																| (1802)  ~ (all_62_0_92 = 0)
% 224.22/173.04  																																																																| (1835)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtlseqdt0(xp, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.04  																																																																|
% 224.22/173.04  																																																																	| Instantiating formula (10) with xn, all_0_3_3, 0, all_62_0_92 and discharging atoms sdtlseqdt0(xn, all_0_3_3) = all_62_0_92, sdtlseqdt0(xn, all_0_3_3) = 0, yields:
% 224.22/173.04  																																																																	| (1832) all_62_0_92 = 0
% 224.22/173.04  																																																																	|
% 224.22/173.04  																																																																	| Equations (1832) can reduce 1802 to:
% 224.22/173.04  																																																																	| (197) $false
% 224.22/173.04  																																																																	|
% 224.22/173.04  																																																																	|-The branch is then unsatisfiable
% 224.22/173.04  																																																															|-Branch two:
% 224.22/173.04  																																																															| (1832) all_62_0_92 = 0
% 224.22/173.04  																																																															| (14065)  ~ (all_62_1_93 = 0) |  ~ (all_62_2_94 = 0)
% 224.22/173.04  																																																															|
% 224.22/173.04  																																																																+-Applying beta-rule and splitting (14065), into two cases.
% 224.22/173.04  																																																																|-Branch one:
% 224.22/173.04  																																																																| (14083)  ~ (all_62_1_93 = 0)
% 224.22/173.04  																																																																|
% 224.22/173.04  																																																																	| Equations (1240) can reduce 14083 to:
% 224.22/173.04  																																																																	| (197) $false
% 224.22/173.04  																																																																	|
% 224.22/173.04  																																																																	|-The branch is then unsatisfiable
% 224.22/173.04  																																																																|-Branch two:
% 224.22/173.04  																																																																| (1240) all_62_1_93 = 0
% 224.22/173.04  																																																																| (14086)  ~ (all_62_2_94 = 0)
% 224.22/173.04  																																																																|
% 224.22/173.04  																																																																	| Equations (1790) can reduce 14086 to:
% 224.22/173.04  																																																																	| (197) $false
% 224.22/173.04  																																																																	|
% 224.22/173.04  																																																																	|-The branch is then unsatisfiable
% 224.22/173.04  																																																										|-Branch two:
% 224.22/173.04  																																																										| (14088)  ~ (all_99_0_112 = xp)
% 224.22/173.04  																																																										| (14089) all_99_0_112 = sz10 |  ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_99_0_112) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 224.22/173.04  																																																										|
% 224.22/173.04  																																																											+-Applying beta-rule and splitting (14089), into two cases.
% 224.22/173.04  																																																											|-Branch one:
% 224.22/173.04  																																																											| (1540) all_99_0_112 = sz10
% 224.22/173.04  																																																											|
% 224.22/173.04  																																																												| Equations (1540) can reduce 298 to:
% 224.22/173.04  																																																												| (197) $false
% 224.22/173.04  																																																												|
% 224.22/173.04  																																																												|-The branch is then unsatisfiable
% 224.22/173.04  																																																											|-Branch two:
% 224.22/173.04  																																																											| (298)  ~ (all_99_0_112 = sz10)
% 224.22/173.04  																																																											| (14093)  ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_99_0_112) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 224.22/173.04  																																																											|
% 224.22/173.04  																																																												| Instantiating (14093) with all_660_0_685 yields:
% 224.22/173.04  																																																												| (14094) ( ~ (all_660_0_685 = 0) & aNaturalNumber0(all_99_0_112) = all_660_0_685) | ( ~ (all_660_0_685 = 0) & aNaturalNumber0(xp) = all_660_0_685)
% 224.22/173.04  																																																												|
% 224.22/173.04  																																																												+-Applying beta-rule and splitting (14094), into two cases.
% 224.22/173.04  																																																												|-Branch one:
% 224.22/173.04  																																																												| (14095)  ~ (all_660_0_685 = 0) & aNaturalNumber0(all_99_0_112) = all_660_0_685
% 224.22/173.04  																																																												|
% 224.22/173.04  																																																													| Applying alpha-rule on (14095) yields:
% 224.22/173.04  																																																													| (14096)  ~ (all_660_0_685 = 0)
% 224.22/173.04  																																																													| (14097) aNaturalNumber0(all_99_0_112) = all_660_0_685
% 224.22/173.04  																																																													|
% 224.22/173.04  																																																													| Instantiating formula (28) with all_99_0_112, all_660_0_685, 0 and discharging atoms aNaturalNumber0(all_99_0_112) = all_660_0_685, aNaturalNumber0(all_99_0_112) = 0, yields:
% 224.22/173.04  																																																													| (14098) all_660_0_685 = 0
% 224.22/173.04  																																																													|
% 224.22/173.04  																																																													| Equations (14098) can reduce 14096 to:
% 224.22/173.04  																																																													| (197) $false
% 224.22/173.04  																																																													|
% 224.22/173.04  																																																													|-The branch is then unsatisfiable
% 224.22/173.04  																																																												|-Branch two:
% 224.22/173.05  																																																												| (14100)  ~ (all_660_0_685 = 0) & aNaturalNumber0(xp) = all_660_0_685
% 224.22/173.05  																																																												|
% 224.22/173.05  																																																													| Applying alpha-rule on (14100) yields:
% 224.22/173.05  																																																													| (14096)  ~ (all_660_0_685 = 0)
% 224.22/173.05  																																																													| (14102) aNaturalNumber0(xp) = all_660_0_685
% 224.22/173.05  																																																													|
% 224.22/173.05  																																																													| Instantiating formula (28) with xp, all_660_0_685, 0 and discharging atoms aNaturalNumber0(xp) = all_660_0_685, aNaturalNumber0(xp) = 0, yields:
% 224.22/173.05  																																																													| (14098) all_660_0_685 = 0
% 224.22/173.05  																																																													|
% 224.22/173.05  																																																													| Equations (14098) can reduce 14096 to:
% 224.22/173.05  																																																													| (197) $false
% 224.22/173.05  																																																													|
% 224.22/173.05  																																																													|-The branch is then unsatisfiable
% 224.22/173.05  																																																									|-Branch two:
% 224.22/173.05  																																																									| (14105)  ~ (all_34_2_54 = all_0_3_3)
% 224.22/173.05  																																																									| (14106)  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_34_2_54) = v0) | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))))
% 224.22/173.05  																																																									|
% 224.22/173.05  																																																										| Instantiating (14106) with all_567_0_686, all_567_1_687, all_567_2_688 yields:
% 224.22/173.05  																																																										| (14107) ( ~ (all_567_2_688 = 0) & aNaturalNumber0(all_34_2_54) = all_567_2_688) | (doDivides0(xr, xn) = all_567_0_686 & aNaturalNumber0(xr) = all_567_2_688 & aNaturalNumber0(xn) = all_567_1_687 & ( ~ (all_567_0_686 = 0) |  ~ (all_567_1_687 = 0) |  ~ (all_567_2_688 = 0)))
% 224.22/173.05  																																																										|
% 224.22/173.05  																																																										+-Applying beta-rule and splitting (14107), into two cases.
% 224.22/173.05  																																																										|-Branch one:
% 224.22/173.05  																																																										| (14108)  ~ (all_567_2_688 = 0) & aNaturalNumber0(all_34_2_54) = all_567_2_688
% 224.22/173.05  																																																										|
% 224.22/173.05  																																																											| Applying alpha-rule on (14108) yields:
% 224.22/173.05  																																																											| (14109)  ~ (all_567_2_688 = 0)
% 224.22/173.05  																																																											| (14110) aNaturalNumber0(all_34_2_54) = all_567_2_688
% 224.22/173.05  																																																											|
% 224.22/173.05  																																																											| Instantiating formula (28) with all_34_2_54, all_567_2_688, 0 and discharging atoms aNaturalNumber0(all_34_2_54) = all_567_2_688, aNaturalNumber0(all_34_2_54) = 0, yields:
% 224.22/173.05  																																																											| (14111) all_567_2_688 = 0
% 224.22/173.05  																																																											|
% 224.22/173.05  																																																											| Equations (14111) can reduce 14109 to:
% 224.22/173.05  																																																											| (197) $false
% 224.22/173.05  																																																											|
% 224.22/173.05  																																																											|-The branch is then unsatisfiable
% 224.22/173.05  																																																										|-Branch two:
% 224.22/173.05  																																																										| (14113) doDivides0(xr, xn) = all_567_0_686 & aNaturalNumber0(xr) = all_567_2_688 & aNaturalNumber0(xn) = all_567_1_687 & ( ~ (all_567_0_686 = 0) |  ~ (all_567_1_687 = 0) |  ~ (all_567_2_688 = 0))
% 224.22/173.05  																																																										|
% 224.22/173.05  																																																											| Applying alpha-rule on (14113) yields:
% 224.22/173.05  																																																											| (14114) doDivides0(xr, xn) = all_567_0_686
% 224.22/173.05  																																																											| (14115) aNaturalNumber0(xr) = all_567_2_688
% 224.22/173.05  																																																											| (14116) aNaturalNumber0(xn) = all_567_1_687
% 224.22/173.05  																																																											| (14117)  ~ (all_567_0_686 = 0) |  ~ (all_567_1_687 = 0) |  ~ (all_567_2_688 = 0)
% 224.22/173.05  																																																											|
% 224.22/173.05  																																																											| Instantiating formula (79) with xr, xn, all_567_0_686, 0 and discharging atoms doDivides0(xr, xn) = all_567_0_686, doDivides0(xr, xn) = 0, yields:
% 224.22/173.06  																																																											| (14118) all_567_0_686 = 0
% 224.22/173.06  																																																											|
% 224.22/173.06  																																																											| Instantiating formula (28) with xr, all_567_2_688, 0 and discharging atoms aNaturalNumber0(xr) = all_567_2_688, aNaturalNumber0(xr) = 0, yields:
% 224.22/173.06  																																																											| (14111) all_567_2_688 = 0
% 224.22/173.06  																																																											|
% 224.22/173.06  																																																											| Instantiating formula (28) with xn, all_567_1_687, 0 and discharging atoms aNaturalNumber0(xn) = all_567_1_687, aNaturalNumber0(xn) = 0, yields:
% 224.22/173.06  																																																											| (14120) all_567_1_687 = 0
% 224.22/173.06  																																																											|
% 224.22/173.06  																																																											+-Applying beta-rule and splitting (14117), into two cases.
% 224.22/173.06  																																																											|-Branch one:
% 224.22/173.06  																																																											| (14121)  ~ (all_567_0_686 = 0)
% 224.22/173.06  																																																											|
% 224.22/173.06  																																																												| Equations (14118) can reduce 14121 to:
% 224.22/173.06  																																																												| (197) $false
% 224.22/173.06  																																																												|
% 224.22/173.06  																																																												|-The branch is then unsatisfiable
% 224.22/173.06  																																																											|-Branch two:
% 224.22/173.06  																																																											| (14118) all_567_0_686 = 0
% 224.22/173.06  																																																											| (14124)  ~ (all_567_1_687 = 0) |  ~ (all_567_2_688 = 0)
% 224.22/173.06  																																																											|
% 224.22/173.06  																																																												+-Applying beta-rule and splitting (14124), into two cases.
% 224.22/173.06  																																																												|-Branch one:
% 224.22/173.06  																																																												| (14125)  ~ (all_567_1_687 = 0)
% 224.22/173.06  																																																												|
% 224.22/173.06  																																																													| Equations (14120) can reduce 14125 to:
% 224.22/173.06  																																																													| (197) $false
% 224.22/173.06  																																																													|
% 224.22/173.06  																																																													|-The branch is then unsatisfiable
% 224.22/173.06  																																																												|-Branch two:
% 224.22/173.06  																																																												| (14120) all_567_1_687 = 0
% 224.22/173.06  																																																												| (14109)  ~ (all_567_2_688 = 0)
% 224.22/173.06  																																																												|
% 224.22/173.06  																																																													| Equations (14111) can reduce 14109 to:
% 224.22/173.06  																																																													| (197) $false
% 224.22/173.06  																																																													|
% 224.22/173.06  																																																													|-The branch is then unsatisfiable
% 224.22/173.06  																																																							|-Branch two:
% 224.22/173.06  																																																							| (14130) sdtasdt0(sz00, xn) = all_0_7_7
% 224.22/173.06  																																																							| (14131)  ? [v0] :  ? [v1] : (sdtasdt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_7_7 = sz00)))
% 224.22/173.06  																																																							|
% 224.22/173.06  																																																								| Instantiating (14131) with all_535_0_689, all_535_1_690 yields:
% 224.22/173.06  																																																								| (14132) sdtasdt0(xn, sz00) = all_535_0_689 & aNaturalNumber0(xn) = all_535_1_690 & ( ~ (all_535_1_690 = 0) | (all_535_0_689 = sz00 & all_0_7_7 = sz00))
% 224.22/173.06  																																																								|
% 224.22/173.06  																																																								| Applying alpha-rule on (14132) yields:
% 224.22/173.06  																																																								| (14133) sdtasdt0(xn, sz00) = all_535_0_689
% 224.22/173.06  																																																								| (14134) aNaturalNumber0(xn) = all_535_1_690
% 224.22/173.06  																																																								| (14135)  ~ (all_535_1_690 = 0) | (all_535_0_689 = sz00 & all_0_7_7 = sz00)
% 224.22/173.06  																																																								|
% 224.22/173.06  																																																								+-Applying beta-rule and splitting (14135), into two cases.
% 224.22/173.06  																																																								|-Branch one:
% 224.22/173.06  																																																								| (14136)  ~ (all_535_1_690 = 0)
% 224.22/173.06  																																																								|
% 224.22/173.06  																																																									| Instantiating formula (28) with xn, all_535_1_690, 0 and discharging atoms aNaturalNumber0(xn) = all_535_1_690, aNaturalNumber0(xn) = 0, yields:
% 224.22/173.06  																																																									| (14137) all_535_1_690 = 0
% 224.22/173.06  																																																									|
% 224.22/173.07  																																																									| Equations (14137) can reduce 14136 to:
% 224.22/173.07  																																																									| (197) $false
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									|-The branch is then unsatisfiable
% 224.22/173.07  																																																								|-Branch two:
% 224.22/173.07  																																																								| (14137) all_535_1_690 = 0
% 224.22/173.07  																																																								| (14140) all_535_0_689 = sz00 & all_0_7_7 = sz00
% 224.22/173.07  																																																								|
% 224.22/173.07  																																																									| Applying alpha-rule on (14140) yields:
% 224.22/173.07  																																																									| (14141) all_535_0_689 = sz00
% 224.22/173.07  																																																									| (14142) all_0_7_7 = sz00
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									| Equations (14142) can reduce 1741 to:
% 224.22/173.07  																																																									| (197) $false
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									|-The branch is then unsatisfiable
% 224.22/173.07  																																																					|-Branch two:
% 224.22/173.07  																																																					| (14144) sdtasdt0(xp, all_28_2_36) = xn
% 224.22/173.07  																																																					| (14145) all_28_2_36 = sz00 | all_0_6_6 = 0 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_28_2_36) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.07  																																																					|
% 224.22/173.07  																																																						| From (1663) and (14144) follows:
% 224.22/173.07  																																																						| (14146) sdtasdt0(xp, xk) = xn
% 224.22/173.07  																																																						|
% 224.22/173.07  																																																						+-Applying beta-rule and splitting (1377), into two cases.
% 224.22/173.07  																																																						|-Branch one:
% 224.22/173.07  																																																						| (1748)  ~ (sdtasdt0(xp, all_28_2_36) = xn)
% 224.22/173.07  																																																						|
% 224.22/173.07  																																																							| From (1663) and (1748) follows:
% 224.22/173.07  																																																							| (1749)  ~ (sdtasdt0(xp, xk) = xn)
% 224.22/173.07  																																																							|
% 224.22/173.07  																																																							| Using (14146) and (1749) yields:
% 224.22/173.07  																																																							| (1311) $false
% 224.22/173.07  																																																							|
% 224.22/173.07  																																																							|-The branch is then unsatisfiable
% 224.22/173.07  																																																						|-Branch two:
% 224.22/173.07  																																																						| (14144) sdtasdt0(xp, all_28_2_36) = xn
% 224.22/173.07  																																																						| (14151) all_0_0_0 = 0 |  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_28_2_36) = v0) | (aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 224.22/173.07  																																																						|
% 224.22/173.07  																																																							| From (1663) and (14144) follows:
% 224.22/173.07  																																																							| (14146) sdtasdt0(xp, xk) = xn
% 224.22/173.07  																																																							|
% 224.22/173.07  																																																							+-Applying beta-rule and splitting (14151), into two cases.
% 224.22/173.07  																																																							|-Branch one:
% 224.22/173.07  																																																							| (215) all_0_0_0 = 0
% 224.22/173.07  																																																							|
% 224.22/173.07  																																																								| Equations (215) can reduce 18 to:
% 224.22/173.07  																																																								| (197) $false
% 224.22/173.07  																																																								|
% 224.22/173.07  																																																								|-The branch is then unsatisfiable
% 224.22/173.07  																																																							|-Branch two:
% 224.22/173.07  																																																							| (18)  ~ (all_0_0_0 = 0)
% 224.22/173.07  																																																							| (14156)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_28_2_36) = v0) | (aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 224.22/173.07  																																																							|
% 224.22/173.07  																																																								| Instantiating formula (49) with xp, xk, xn, all_0_7_7 and discharging atoms sdtasdt0(xp, xk) = all_0_7_7, sdtasdt0(xp, xk) = xn, yields:
% 224.22/173.07  																																																								| (13962) all_0_7_7 = xn
% 224.22/173.07  																																																								|
% 224.22/173.07  																																																								| From (13962) and (37) follows:
% 224.22/173.07  																																																								| (14158) doDivides0(xp, xn) = 0
% 224.22/173.07  																																																								|
% 224.22/173.07  																																																								+-Applying beta-rule and splitting (305), into two cases.
% 224.22/173.07  																																																								|-Branch one:
% 224.22/173.07  																																																								| (14159)  ~ (doDivides0(xp, xn) = 0)
% 224.22/173.07  																																																								|
% 224.22/173.07  																																																									| Using (14158) and (14159) yields:
% 224.22/173.07  																																																									| (1311) $false
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									|-The branch is then unsatisfiable
% 224.22/173.07  																																																								|-Branch two:
% 224.22/173.07  																																																								| (14158) doDivides0(xp, xn) = 0
% 224.22/173.07  																																																								| (14162) all_39_1_67 = 0
% 224.22/173.07  																																																								|
% 224.22/173.07  																																																									| Combining equations (306,14162) yields a new equation:
% 224.22/173.07  																																																									| (14163) all_0_0_0 = 0
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									| Simplifying 14163 yields:
% 224.22/173.07  																																																									| (215) all_0_0_0 = 0
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									| Equations (215) can reduce 18 to:
% 224.22/173.07  																																																									| (197) $false
% 224.22/173.07  																																																									|
% 224.22/173.07  																																																									|-The branch is then unsatisfiable
% 224.22/173.08  																																											|-Branch two:
% 224.22/173.08  																																											| (14166) aNaturalNumber0(all_99_0_112) = all_249_2_193 & aNaturalNumber0(xp) = all_249_1_192 & ( ~ (all_249_1_192 = 0) |  ~ (all_249_2_193 = 0))
% 224.22/173.08  																																											|
% 224.22/173.08  																																												| Applying alpha-rule on (14166) yields:
% 224.22/173.08  																																												| (14167) aNaturalNumber0(all_99_0_112) = all_249_2_193
% 224.22/173.08  																																												| (14168) aNaturalNumber0(xp) = all_249_1_192
% 224.22/173.08  																																												| (14169)  ~ (all_249_1_192 = 0) |  ~ (all_249_2_193 = 0)
% 224.22/173.08  																																												|
% 224.22/173.08  																																												+-Applying beta-rule and splitting (1407), into two cases.
% 224.22/173.08  																																												|-Branch one:
% 224.22/173.08  																																												| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 224.22/173.08  																																												|
% 224.22/173.08  																																													| Using (1665) and (1670) yields:
% 224.22/173.08  																																													| (1311) $false
% 224.22/173.08  																																													|
% 224.22/173.08  																																													|-The branch is then unsatisfiable
% 224.22/173.08  																																												|-Branch two:
% 224.22/173.08  																																												| (1665) aNaturalNumber0(xk) = 0
% 224.22/173.08  																																												| (1687) xk = sz10 | xk = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 224.22/173.08  																																												|
% 224.22/173.08  																																													+-Applying beta-rule and splitting (1405), into two cases.
% 224.22/173.08  																																													|-Branch one:
% 224.22/173.08  																																													| (1688) all_28_2_36 = sz00
% 224.22/173.08  																																													|
% 224.22/173.08  																																														| Combining equations (1663,1688) yields a new equation:
% 224.22/173.08  																																														| (1689) xk = sz00
% 224.22/173.08  																																														|
% 224.22/173.08  																																														| Simplifying 1689 yields:
% 224.22/173.08  																																														| (1690) xk = sz00
% 224.22/173.08  																																														|
% 224.22/173.08  																																														| Equations (1690) can reduce 27 to:
% 224.22/173.08  																																														| (197) $false
% 224.22/173.08  																																														|
% 224.22/173.08  																																														|-The branch is then unsatisfiable
% 224.22/173.08  																																													|-Branch two:
% 224.22/173.08  																																													| (1692)  ~ (all_28_2_36 = sz00)
% 224.22/173.08  																																													| (1693) all_28_2_36 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_28_2_36) = 0 & aNaturalNumber0(v0) = 0)
% 224.22/173.08  																																													|
% 224.22/173.08  																																														| Equations (1663) can reduce 1692 to:
% 224.22/173.08  																																														| (27)  ~ (xk = sz00)
% 224.22/173.08  																																														|
% 224.22/173.08  																																														+-Applying beta-rule and splitting (1687), into two cases.
% 224.22/173.08  																																														|-Branch one:
% 224.22/173.08  																																														| (1690) xk = sz00
% 224.22/173.08  																																														|
% 224.22/173.08  																																															| Equations (1690) can reduce 27 to:
% 224.22/173.08  																																															| (197) $false
% 224.22/173.08  																																															|
% 224.22/173.08  																																															|-The branch is then unsatisfiable
% 224.22/173.08  																																														|-Branch two:
% 224.22/173.08  																																														| (27)  ~ (xk = sz00)
% 224.22/173.08  																																														| (1698) xk = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 224.22/173.08  																																														|
% 224.22/173.08  																																															+-Applying beta-rule and splitting (1366), into two cases.
% 224.22/173.08  																																															|-Branch one:
% 224.22/173.08  																																															| (1690) xk = sz00
% 224.22/173.08  																																															|
% 224.22/173.08  																																																| Equations (1690) can reduce 27 to:
% 224.22/173.08  																																																| (197) $false
% 224.22/173.08  																																																|
% 224.22/173.08  																																																|-The branch is then unsatisfiable
% 224.22/173.08  																																															|-Branch two:
% 224.22/173.08  																																															| (27)  ~ (xk = sz00)
% 224.22/173.08  																																															| (1717) all_52_0_85 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.08  																																															|
% 224.22/173.08  																																																+-Applying beta-rule and splitting (1717), into two cases.
% 224.22/173.08  																																																|-Branch one:
% 224.22/173.08  																																																| (1722) all_52_0_85 = 0
% 224.22/173.08  																																																|
% 224.22/173.08  																																																	| Equations (1722) can reduce 1676 to:
% 224.22/173.08  																																																	| (197) $false
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	|-The branch is then unsatisfiable
% 224.22/173.08  																																																|-Branch two:
% 224.22/173.08  																																																| (1676)  ~ (all_52_0_85 = 0)
% 224.22/173.08  																																																| (1725)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.08  																																																|
% 224.22/173.08  																																																	| Instantiating (1725) with all_448_0_771, all_448_1_772, all_448_2_773 yields:
% 224.22/173.08  																																																	| (14193) doDivides0(xp, xk) = all_448_0_771 & aNaturalNumber0(xk) = all_448_1_772 & aNaturalNumber0(xp) = all_448_2_773 & ( ~ (all_448_0_771 = 0) |  ~ (all_448_1_772 = 0) |  ~ (all_448_2_773 = 0))
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	| Applying alpha-rule on (14193) yields:
% 224.22/173.08  																																																	| (14194) doDivides0(xp, xk) = all_448_0_771
% 224.22/173.08  																																																	| (14195) aNaturalNumber0(xk) = all_448_1_772
% 224.22/173.08  																																																	| (14196) aNaturalNumber0(xp) = all_448_2_773
% 224.22/173.08  																																																	| (14197)  ~ (all_448_0_771 = 0) |  ~ (all_448_1_772 = 0) |  ~ (all_448_2_773 = 0)
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	| Instantiating formula (28) with all_99_0_112, all_249_2_193, 0 and discharging atoms aNaturalNumber0(all_99_0_112) = all_249_2_193, aNaturalNumber0(all_99_0_112) = 0, yields:
% 224.22/173.08  																																																	| (14198) all_249_2_193 = 0
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	| Instantiating formula (28) with xp, all_448_2_773, 0 and discharging atoms aNaturalNumber0(xp) = all_448_2_773, aNaturalNumber0(xp) = 0, yields:
% 224.22/173.08  																																																	| (14199) all_448_2_773 = 0
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	| Instantiating formula (28) with xp, all_249_1_192, all_448_2_773 and discharging atoms aNaturalNumber0(xp) = all_448_2_773, aNaturalNumber0(xp) = all_249_1_192, yields:
% 224.22/173.08  																																																	| (14200) all_448_2_773 = all_249_1_192
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	| Combining equations (14199,14200) yields a new equation:
% 224.22/173.08  																																																	| (1681) all_249_1_192 = 0
% 224.22/173.08  																																																	|
% 224.22/173.08  																																																	+-Applying beta-rule and splitting (14169), into two cases.
% 224.22/173.08  																																																	|-Branch one:
% 224.22/173.09  																																																	| (14202)  ~ (all_249_1_192 = 0)
% 224.22/173.09  																																																	|
% 224.22/173.09  																																																		| Equations (1681) can reduce 14202 to:
% 224.22/173.09  																																																		| (197) $false
% 224.22/173.09  																																																		|
% 224.22/173.09  																																																		|-The branch is then unsatisfiable
% 224.22/173.09  																																																	|-Branch two:
% 224.22/173.09  																																																	| (1681) all_249_1_192 = 0
% 224.22/173.09  																																																	| (14205)  ~ (all_249_2_193 = 0)
% 224.22/173.09  																																																	|
% 224.22/173.09  																																																		| Equations (14198) can reduce 14205 to:
% 224.22/173.09  																																																		| (197) $false
% 224.22/173.09  																																																		|
% 224.22/173.09  																																																		|-The branch is then unsatisfiable
% 224.22/173.09  																																										|-Branch two:
% 224.22/173.09  																																										| (14207) sdtasdt0(xp, all_28_2_36) = sz00
% 224.22/173.09  																																										| (14208) all_28_2_36 = sz00 | xp = sz00 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_28_2_36) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.09  																																										|
% 224.22/173.09  																																											+-Applying beta-rule and splitting (14208), into two cases.
% 224.22/173.09  																																											|-Branch one:
% 224.22/173.09  																																											| (1688) all_28_2_36 = sz00
% 224.22/173.09  																																											|
% 224.22/173.09  																																												| Combining equations (1663,1688) yields a new equation:
% 224.22/173.09  																																												| (1689) xk = sz00
% 224.22/173.09  																																												|
% 224.22/173.09  																																												| Simplifying 1689 yields:
% 224.22/173.09  																																												| (1690) xk = sz00
% 224.22/173.09  																																												|
% 224.22/173.09  																																												| Equations (1690) can reduce 27 to:
% 224.22/173.09  																																												| (197) $false
% 224.22/173.09  																																												|
% 224.22/173.09  																																												|-The branch is then unsatisfiable
% 224.22/173.09  																																											|-Branch two:
% 224.22/173.09  																																											| (1692)  ~ (all_28_2_36 = sz00)
% 224.22/173.09  																																											| (14214) xp = sz00 |  ? [v0] :  ? [v1] : (aNaturalNumber0(all_28_2_36) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.09  																																											|
% 224.22/173.09  																																												| Equations (1663) can reduce 1692 to:
% 224.22/173.09  																																												| (27)  ~ (xk = sz00)
% 224.22/173.09  																																												|
% 224.22/173.09  																																												+-Applying beta-rule and splitting (14214), into two cases.
% 224.22/173.09  																																												|-Branch one:
% 224.22/173.09  																																												| (278) xp = sz00
% 224.22/173.09  																																												|
% 224.22/173.09  																																													| Equations (278) can reduce 101 to:
% 224.22/173.09  																																													| (197) $false
% 224.22/173.09  																																													|
% 224.22/173.09  																																													|-The branch is then unsatisfiable
% 224.22/173.09  																																												|-Branch two:
% 224.22/173.09  																																												| (101)  ~ (xp = sz00)
% 224.22/173.09  																																												| (14219)  ? [v0] :  ? [v1] : (aNaturalNumber0(all_28_2_36) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.09  																																												|
% 224.22/173.09  																																													| Instantiating (14219) with all_356_0_775, all_356_1_776 yields:
% 224.22/173.09  																																													| (14220) aNaturalNumber0(all_28_2_36) = all_356_0_775 & aNaturalNumber0(xp) = all_356_1_776 & ( ~ (all_356_0_775 = 0) |  ~ (all_356_1_776 = 0))
% 224.22/173.09  																																													|
% 224.22/173.09  																																													| Applying alpha-rule on (14220) yields:
% 224.22/173.09  																																													| (14221) aNaturalNumber0(all_28_2_36) = all_356_0_775
% 224.22/173.09  																																													| (14222) aNaturalNumber0(xp) = all_356_1_776
% 224.22/173.09  																																													| (14223)  ~ (all_356_0_775 = 0) |  ~ (all_356_1_776 = 0)
% 224.22/173.09  																																													|
% 224.22/173.09  																																													| From (1663) and (14221) follows:
% 224.22/173.09  																																													| (14224) aNaturalNumber0(xk) = all_356_0_775
% 224.22/173.09  																																													|
% 224.22/173.09  																																													+-Applying beta-rule and splitting (1407), into two cases.
% 224.22/173.09  																																													|-Branch one:
% 224.22/173.09  																																													| (1670)  ~ (aNaturalNumber0(xk) = 0)
% 224.22/173.09  																																													|
% 224.22/173.09  																																														| Using (1665) and (1670) yields:
% 224.22/173.09  																																														| (1311) $false
% 224.22/173.09  																																														|
% 224.22/173.09  																																														|-The branch is then unsatisfiable
% 224.22/173.09  																																													|-Branch two:
% 224.22/173.09  																																													| (1665) aNaturalNumber0(xk) = 0
% 224.22/173.09  																																													| (1687) xk = sz10 | xk = sz00 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 224.22/173.09  																																													|
% 224.22/173.09  																																														+-Applying beta-rule and splitting (1405), into two cases.
% 224.22/173.09  																																														|-Branch one:
% 224.22/173.09  																																														| (1688) all_28_2_36 = sz00
% 224.22/173.09  																																														|
% 224.22/173.09  																																															| Combining equations (1688,1663) yields a new equation:
% 224.22/173.09  																																															| (1690) xk = sz00
% 224.22/173.09  																																															|
% 224.22/173.09  																																															| Equations (1690) can reduce 27 to:
% 224.22/173.09  																																															| (197) $false
% 224.22/173.09  																																															|
% 224.22/173.09  																																															|-The branch is then unsatisfiable
% 224.22/173.09  																																														|-Branch two:
% 224.22/173.09  																																														| (1692)  ~ (all_28_2_36 = sz00)
% 224.22/173.09  																																														| (1693) all_28_2_36 = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_28_2_36) = 0 & aNaturalNumber0(v0) = 0)
% 224.22/173.09  																																														|
% 224.22/173.09  																																															| Equations (1663) can reduce 1692 to:
% 224.22/173.09  																																															| (27)  ~ (xk = sz00)
% 224.22/173.09  																																															|
% 224.22/173.09  																																															+-Applying beta-rule and splitting (1687), into two cases.
% 224.22/173.09  																																															|-Branch one:
% 224.22/173.09  																																															| (1690) xk = sz00
% 224.22/173.09  																																															|
% 224.22/173.09  																																																| Equations (1690) can reduce 27 to:
% 224.22/173.09  																																																| (197) $false
% 224.22/173.09  																																																|
% 224.22/173.09  																																																|-The branch is then unsatisfiable
% 224.22/173.09  																																															|-Branch two:
% 224.22/173.09  																																															| (27)  ~ (xk = sz00)
% 224.22/173.09  																																															| (1698) xk = sz10 |  ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 224.22/173.09  																																															|
% 224.22/173.09  																																																+-Applying beta-rule and splitting (1366), into two cases.
% 224.22/173.09  																																																|-Branch one:
% 224.22/173.09  																																																| (1690) xk = sz00
% 224.22/173.09  																																																|
% 224.22/173.09  																																																	| Equations (1690) can reduce 27 to:
% 224.22/173.09  																																																	| (197) $false
% 224.22/173.09  																																																	|
% 224.22/173.09  																																																	|-The branch is then unsatisfiable
% 224.22/173.09  																																																|-Branch two:
% 224.22/173.09  																																																| (27)  ~ (xk = sz00)
% 224.22/173.09  																																																| (1717) all_52_0_85 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.09  																																																|
% 224.22/173.09  																																																	+-Applying beta-rule and splitting (1717), into two cases.
% 224.22/173.09  																																																	|-Branch one:
% 224.22/173.09  																																																	| (1722) all_52_0_85 = 0
% 224.22/173.09  																																																	|
% 224.22/173.09  																																																		| Equations (1722) can reduce 1676 to:
% 224.22/173.09  																																																		| (197) $false
% 224.22/173.09  																																																		|
% 224.22/173.09  																																																		|-The branch is then unsatisfiable
% 224.22/173.09  																																																	|-Branch two:
% 224.22/173.09  																																																	| (1676)  ~ (all_52_0_85 = 0)
% 224.22/173.09  																																																	| (1725)  ? [v0] :  ? [v1] :  ? [v2] : (doDivides0(xp, xk) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 224.22/173.09  																																																	|
% 224.22/173.09  																																																		| Instantiating (1725) with all_489_0_796, all_489_1_797, all_489_2_798 yields:
% 224.22/173.10  																																																		| (14247) doDivides0(xp, xk) = all_489_0_796 & aNaturalNumber0(xk) = all_489_1_797 & aNaturalNumber0(xp) = all_489_2_798 & ( ~ (all_489_0_796 = 0) |  ~ (all_489_1_797 = 0) |  ~ (all_489_2_798 = 0))
% 224.22/173.10  																																																		|
% 224.22/173.10  																																																		| Applying alpha-rule on (14247) yields:
% 224.22/173.10  																																																		| (14248) doDivides0(xp, xk) = all_489_0_796
% 224.30/173.10  																																																		| (14249) aNaturalNumber0(xk) = all_489_1_797
% 224.30/173.10  																																																		| (14250) aNaturalNumber0(xp) = all_489_2_798
% 224.30/173.10  																																																		| (14251)  ~ (all_489_0_796 = 0) |  ~ (all_489_1_797 = 0) |  ~ (all_489_2_798 = 0)
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Instantiating formula (28) with xk, all_489_1_797, 0 and discharging atoms aNaturalNumber0(xk) = all_489_1_797, aNaturalNumber0(xk) = 0, yields:
% 224.30/173.10  																																																		| (14252) all_489_1_797 = 0
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Instantiating formula (28) with xk, all_356_0_775, all_489_1_797 and discharging atoms aNaturalNumber0(xk) = all_489_1_797, aNaturalNumber0(xk) = all_356_0_775, yields:
% 224.30/173.10  																																																		| (14253) all_489_1_797 = all_356_0_775
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Instantiating formula (28) with xp, all_489_2_798, 0 and discharging atoms aNaturalNumber0(xp) = all_489_2_798, aNaturalNumber0(xp) = 0, yields:
% 224.30/173.10  																																																		| (14254) all_489_2_798 = 0
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Instantiating formula (28) with xp, all_356_1_776, all_489_2_798 and discharging atoms aNaturalNumber0(xp) = all_489_2_798, aNaturalNumber0(xp) = all_356_1_776, yields:
% 224.30/173.10  																																																		| (14255) all_489_2_798 = all_356_1_776
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Combining equations (14252,14253) yields a new equation:
% 224.30/173.10  																																																		| (14256) all_356_0_775 = 0
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Combining equations (14255,14254) yields a new equation:
% 224.30/173.10  																																																		| (14257) all_356_1_776 = 0
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		| Simplifying 14257 yields:
% 224.30/173.10  																																																		| (14258) all_356_1_776 = 0
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																		+-Applying beta-rule and splitting (14223), into two cases.
% 224.30/173.10  																																																		|-Branch one:
% 224.30/173.10  																																																		| (14259)  ~ (all_356_0_775 = 0)
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																			| Equations (14256) can reduce 14259 to:
% 224.30/173.10  																																																			| (197) $false
% 224.30/173.10  																																																			|
% 224.30/173.10  																																																			|-The branch is then unsatisfiable
% 224.30/173.10  																																																		|-Branch two:
% 224.30/173.10  																																																		| (14256) all_356_0_775 = 0
% 224.30/173.10  																																																		| (14262)  ~ (all_356_1_776 = 0)
% 224.30/173.10  																																																		|
% 224.30/173.10  																																																			| Equations (14258) can reduce 14262 to:
% 224.30/173.10  																																																			| (197) $false
% 224.30/173.10  																																																			|
% 224.30/173.10  																																																			|-The branch is then unsatisfiable
% 224.30/173.11  																																									|-Branch two:
% 224.30/173.11  																																									| (1722) all_52_0_85 = 0
% 224.30/173.11  																																									| (14265)  ~ (all_52_1_86 = 0) |  ~ (all_52_2_87 = 0)
% 224.30/173.11  																																									|
% 224.30/173.11  																																										+-Applying beta-rule and splitting (14265), into two cases.
% 224.30/173.11  																																										|-Branch one:
% 224.30/173.11  																																										| (14266)  ~ (all_52_1_86 = 0)
% 224.30/173.11  																																										|
% 224.30/173.11  																																											| Equations (1238) can reduce 14266 to:
% 224.30/173.11  																																											| (197) $false
% 224.30/173.11  																																											|
% 224.30/173.11  																																											|-The branch is then unsatisfiable
% 224.30/173.11  																																										|-Branch two:
% 224.30/173.11  																																										| (1238) all_52_1_86 = 0
% 224.30/173.11  																																										| (14269)  ~ (all_52_2_87 = 0)
% 224.30/173.11  																																										|
% 224.30/173.11  																																											| Equations (1674) can reduce 14269 to:
% 224.30/173.11  																																											| (197) $false
% 224.30/173.11  																																											|
% 224.30/173.11  																																											|-The branch is then unsatisfiable
% 224.30/173.11  																																							|-Branch two:
% 224.30/173.11  																																							| (14271)  ~ (all_94_0_111 = xr)
% 224.30/173.11  																																							| (14272) all_94_0_111 = sz10 |  ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_94_0_111) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0))
% 224.30/173.11  																																							|
% 224.30/173.11  																																								+-Applying beta-rule and splitting (14272), into two cases.
% 224.30/173.11  																																								|-Branch one:
% 224.30/173.11  																																								| (1536) all_94_0_111 = sz10
% 224.30/173.11  																																								|
% 224.30/173.11  																																									| Equations (1536) can reduce 300 to:
% 224.30/173.11  																																									| (197) $false
% 224.30/173.11  																																									|
% 224.30/173.11  																																									|-The branch is then unsatisfiable
% 224.30/173.11  																																								|-Branch two:
% 224.30/173.11  																																								| (300)  ~ (all_94_0_111 = sz10)
% 224.30/173.11  																																								| (14276)  ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_94_0_111) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0))
% 224.30/173.11  																																								|
% 224.30/173.11  																																									| Instantiating (14276) with all_328_0_804 yields:
% 224.30/173.11  																																									| (14277) ( ~ (all_328_0_804 = 0) & aNaturalNumber0(all_94_0_111) = all_328_0_804) | ( ~ (all_328_0_804 = 0) & aNaturalNumber0(xr) = all_328_0_804)
% 224.30/173.11  																																									|
% 224.30/173.11  																																									+-Applying beta-rule and splitting (14277), into two cases.
% 224.30/173.11  																																									|-Branch one:
% 224.30/173.11  																																									| (14278)  ~ (all_328_0_804 = 0) & aNaturalNumber0(all_94_0_111) = all_328_0_804
% 224.30/173.11  																																									|
% 224.30/173.11  																																										| Applying alpha-rule on (14278) yields:
% 224.30/173.11  																																										| (14279)  ~ (all_328_0_804 = 0)
% 224.30/173.11  																																										| (14280) aNaturalNumber0(all_94_0_111) = all_328_0_804
% 224.30/173.11  																																										|
% 224.30/173.11  																																										| Instantiating formula (28) with all_94_0_111, all_328_0_804, 0 and discharging atoms aNaturalNumber0(all_94_0_111) = all_328_0_804, aNaturalNumber0(all_94_0_111) = 0, yields:
% 224.30/173.11  																																										| (14281) all_328_0_804 = 0
% 224.30/173.11  																																										|
% 224.30/173.11  																																										| Equations (14281) can reduce 14279 to:
% 224.30/173.11  																																										| (197) $false
% 224.30/173.11  																																										|
% 224.30/173.11  																																										|-The branch is then unsatisfiable
% 224.30/173.11  																																									|-Branch two:
% 224.30/173.11  																																									| (14283)  ~ (all_328_0_804 = 0) & aNaturalNumber0(xr) = all_328_0_804
% 224.30/173.11  																																									|
% 224.30/173.11  																																										| Applying alpha-rule on (14283) yields:
% 224.30/173.11  																																										| (14279)  ~ (all_328_0_804 = 0)
% 224.30/173.11  																																										| (14285) aNaturalNumber0(xr) = all_328_0_804
% 224.30/173.11  																																										|
% 224.30/173.11  																																										| Instantiating formula (28) with xr, all_328_0_804, 0 and discharging atoms aNaturalNumber0(xr) = all_328_0_804, aNaturalNumber0(xr) = 0, yields:
% 224.30/173.11  																																										| (14281) all_328_0_804 = 0
% 224.30/173.11  																																										|
% 224.30/173.11  																																										| Equations (14281) can reduce 14279 to:
% 224.30/173.11  																																										| (197) $false
% 224.30/173.11  																																										|
% 224.30/173.11  																																										|-The branch is then unsatisfiable
% 224.30/173.12  																																						|-Branch two:
% 224.30/173.12  																																						| (14288)  ~ (all_28_2_36 = xk)
% 224.30/173.12  																																						| (14289)  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_28_2_36) = v0) | (doDivides0(xp, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0))))
% 224.30/173.12  																																						|
% 224.30/173.12  																																							| Instantiating (14289) with all_304_0_828, all_304_1_829, all_304_2_830 yields:
% 224.30/173.12  																																							| (14290) ( ~ (all_304_2_830 = 0) & aNaturalNumber0(all_28_2_36) = all_304_2_830) | (doDivides0(xp, all_0_7_7) = all_304_0_828 & aNaturalNumber0(all_0_7_7) = all_304_1_829 & aNaturalNumber0(xp) = all_304_2_830 & ( ~ (all_304_0_828 = 0) |  ~ (all_304_1_829 = 0) |  ~ (all_304_2_830 = 0)))
% 224.30/173.12  																																							|
% 224.30/173.12  																																							+-Applying beta-rule and splitting (14290), into two cases.
% 224.30/173.12  																																							|-Branch one:
% 224.30/173.12  																																							| (14291)  ~ (all_304_2_830 = 0) & aNaturalNumber0(all_28_2_36) = all_304_2_830
% 224.30/173.12  																																							|
% 224.30/173.12  																																								| Applying alpha-rule on (14291) yields:
% 224.30/173.12  																																								| (14292)  ~ (all_304_2_830 = 0)
% 224.30/173.12  																																								| (14293) aNaturalNumber0(all_28_2_36) = all_304_2_830
% 224.30/173.12  																																								|
% 224.30/173.12  																																								| Instantiating formula (28) with all_28_2_36, all_304_2_830, 0 and discharging atoms aNaturalNumber0(all_28_2_36) = all_304_2_830, aNaturalNumber0(all_28_2_36) = 0, yields:
% 224.30/173.12  																																								| (14294) all_304_2_830 = 0
% 224.30/173.12  																																								|
% 224.30/173.12  																																								| Equations (14294) can reduce 14292 to:
% 224.30/173.12  																																								| (197) $false
% 224.30/173.12  																																								|
% 224.30/173.12  																																								|-The branch is then unsatisfiable
% 224.30/173.12  																																							|-Branch two:
% 224.30/173.12  																																							| (14296) doDivides0(xp, all_0_7_7) = all_304_0_828 & aNaturalNumber0(all_0_7_7) = all_304_1_829 & aNaturalNumber0(xp) = all_304_2_830 & ( ~ (all_304_0_828 = 0) |  ~ (all_304_1_829 = 0) |  ~ (all_304_2_830 = 0))
% 224.30/173.12  																																							|
% 224.30/173.12  																																								| Applying alpha-rule on (14296) yields:
% 224.30/173.12  																																								| (14297) doDivides0(xp, all_0_7_7) = all_304_0_828
% 224.30/173.12  																																								| (14298) aNaturalNumber0(all_0_7_7) = all_304_1_829
% 224.30/173.12  																																								| (14299) aNaturalNumber0(xp) = all_304_2_830
% 224.30/173.12  																																								| (14300)  ~ (all_304_0_828 = 0) |  ~ (all_304_1_829 = 0) |  ~ (all_304_2_830 = 0)
% 224.30/173.12  																																								|
% 224.30/173.12  																																								| Instantiating formula (79) with xp, all_0_7_7, all_304_0_828, 0 and discharging atoms doDivides0(xp, all_0_7_7) = all_304_0_828, doDivides0(xp, all_0_7_7) = 0, yields:
% 224.30/173.12  																																								| (14301) all_304_0_828 = 0
% 224.30/173.12  																																								|
% 224.30/173.12  																																								| Instantiating formula (28) with all_0_7_7, all_304_1_829, 0 and discharging atoms aNaturalNumber0(all_0_7_7) = all_304_1_829, aNaturalNumber0(all_0_7_7) = 0, yields:
% 224.30/173.12  																																								| (14302) all_304_1_829 = 0
% 224.30/173.12  																																								|
% 224.30/173.12  																																								| Instantiating formula (28) with xp, all_304_2_830, 0 and discharging atoms aNaturalNumber0(xp) = all_304_2_830, aNaturalNumber0(xp) = 0, yields:
% 224.30/173.12  																																								| (14294) all_304_2_830 = 0
% 224.30/173.12  																																								|
% 224.30/173.12  																																								+-Applying beta-rule and splitting (14300), into two cases.
% 224.30/173.12  																																								|-Branch one:
% 224.30/173.12  																																								| (14304)  ~ (all_304_0_828 = 0)
% 224.30/173.12  																																								|
% 224.30/173.12  																																									| Equations (14301) can reduce 14304 to:
% 224.30/173.12  																																									| (197) $false
% 224.30/173.12  																																									|
% 224.30/173.12  																																									|-The branch is then unsatisfiable
% 224.30/173.12  																																								|-Branch two:
% 224.30/173.12  																																								| (14301) all_304_0_828 = 0
% 224.30/173.12  																																								| (14307)  ~ (all_304_1_829 = 0) |  ~ (all_304_2_830 = 0)
% 224.30/173.12  																																								|
% 224.30/173.13  																																									+-Applying beta-rule and splitting (14307), into two cases.
% 224.30/173.13  																																									|-Branch one:
% 224.30/173.13  																																									| (14308)  ~ (all_304_1_829 = 0)
% 224.30/173.13  																																									|
% 224.30/173.13  																																										| Equations (14302) can reduce 14308 to:
% 224.30/173.13  																																										| (197) $false
% 224.30/173.13  																																										|
% 224.30/173.13  																																										|-The branch is then unsatisfiable
% 224.30/173.13  																																									|-Branch two:
% 224.30/173.13  																																									| (14302) all_304_1_829 = 0
% 224.30/173.13  																																									| (14292)  ~ (all_304_2_830 = 0)
% 224.30/173.13  																																									|
% 224.30/173.13  																																										| Equations (14294) can reduce 14292 to:
% 224.30/173.13  																																										| (197) $false
% 224.30/173.13  																																										|
% 224.30/173.13  																																										|-The branch is then unsatisfiable
% 224.30/173.13  																																|-Branch two:
% 224.30/173.13  																																| (14313) aNaturalNumber0(all_0_7_7) = all_41_1_76 & aNaturalNumber0(xr) = all_41_2_77 & ( ~ (all_41_1_76 = 0) |  ~ (all_41_2_77 = 0))
% 224.30/173.13  																																|
% 224.30/173.13  																																	| Applying alpha-rule on (14313) yields:
% 224.30/173.13  																																	| (14314) aNaturalNumber0(all_0_7_7) = all_41_1_76
% 224.30/173.13  																																	| (14315) aNaturalNumber0(xr) = all_41_2_77
% 224.30/173.13  																																	| (14316)  ~ (all_41_1_76 = 0) |  ~ (all_41_2_77 = 0)
% 224.30/173.13  																																	|
% 224.30/173.13  																																	| Instantiating formula (28) with all_0_7_7, all_41_1_76, 0 and discharging atoms aNaturalNumber0(all_0_7_7) = all_41_1_76, aNaturalNumber0(all_0_7_7) = 0, yields:
% 224.30/173.13  																																	| (1359) all_41_1_76 = 0
% 224.30/173.13  																																	|
% 224.30/173.13  																																	| Instantiating formula (28) with xr, all_41_2_77, 0 and discharging atoms aNaturalNumber0(xr) = all_41_2_77, aNaturalNumber0(xr) = 0, yields:
% 224.30/173.13  																																	| (14318) all_41_2_77 = 0
% 224.30/173.13  																																	|
% 224.30/173.13  																																	+-Applying beta-rule and splitting (14316), into two cases.
% 224.30/173.13  																																	|-Branch one:
% 224.30/173.13  																																	| (14319)  ~ (all_41_1_76 = 0)
% 224.30/173.13  																																	|
% 224.30/173.13  																																		| Equations (1359) can reduce 14319 to:
% 224.30/173.13  																																		| (197) $false
% 224.30/173.13  																																		|
% 224.30/173.13  																																		|-The branch is then unsatisfiable
% 224.30/173.13  																																	|-Branch two:
% 224.30/173.13  																																	| (1359) all_41_1_76 = 0
% 224.30/173.13  																																	| (14322)  ~ (all_41_2_77 = 0)
% 224.30/173.13  																																	|
% 224.30/173.13  																																		| Equations (14318) can reduce 14322 to:
% 224.30/173.13  																																		| (197) $false
% 224.30/173.13  																																		|
% 224.30/173.13  																																		|-The branch is then unsatisfiable
% 224.30/173.13  																												|-Branch two:
% 224.30/173.13  																												| (14324) aNaturalNumber0(xr) = all_34_2_54 & aNaturalNumber0(xn) = all_34_1_53 & ( ~ (all_34_1_53 = 0) |  ~ (all_34_2_54 = 0))
% 224.30/173.13  																												|
% 224.30/173.13  																													| Applying alpha-rule on (14324) yields:
% 224.30/173.13  																													| (14325) aNaturalNumber0(xr) = all_34_2_54
% 224.30/173.14  																													| (14326) aNaturalNumber0(xn) = all_34_1_53
% 224.30/173.14  																													| (14327)  ~ (all_34_1_53 = 0) |  ~ (all_34_2_54 = 0)
% 224.30/173.14  																													|
% 224.30/173.14  																													| Instantiating formula (28) with xr, all_34_2_54, 0 and discharging atoms aNaturalNumber0(xr) = all_34_2_54, aNaturalNumber0(xr) = 0, yields:
% 224.30/173.14  																													| (14328) all_34_2_54 = 0
% 224.30/173.14  																													|
% 224.30/173.14  																													| Instantiating formula (28) with xn, all_34_1_53, 0 and discharging atoms aNaturalNumber0(xn) = all_34_1_53, aNaturalNumber0(xn) = 0, yields:
% 224.30/173.14  																													| (1340) all_34_1_53 = 0
% 224.30/173.14  																													|
% 224.30/173.14  																													+-Applying beta-rule and splitting (14327), into two cases.
% 224.30/173.14  																													|-Branch one:
% 224.30/173.14  																													| (14330)  ~ (all_34_1_53 = 0)
% 224.30/173.14  																													|
% 224.30/173.14  																														| Equations (1340) can reduce 14330 to:
% 224.30/173.14  																														| (197) $false
% 224.30/173.14  																														|
% 224.30/173.14  																														|-The branch is then unsatisfiable
% 224.30/173.14  																													|-Branch two:
% 224.30/173.14  																													| (1340) all_34_1_53 = 0
% 224.30/173.14  																													| (14333)  ~ (all_34_2_54 = 0)
% 224.30/173.14  																													|
% 224.30/173.14  																														| Equations (14328) can reduce 14333 to:
% 224.30/173.14  																														| (197) $false
% 224.30/173.14  																														|
% 224.30/173.14  																														|-The branch is then unsatisfiable
% 224.30/173.14  																							|-Branch two:
% 224.30/173.14  																							| (14335) aNaturalNumber0(xp) = all_30_1_41 & aNaturalNumber0(xn) = all_30_2_42 & ( ~ (all_30_1_41 = 0) |  ~ (all_30_2_42 = 0))
% 224.30/173.14  																							|
% 224.30/173.14  																								| Applying alpha-rule on (14335) yields:
% 224.30/173.14  																								| (14336) aNaturalNumber0(xp) = all_30_1_41
% 224.30/173.14  																								| (14337) aNaturalNumber0(xn) = all_30_2_42
% 224.30/173.14  																								| (14338)  ~ (all_30_1_41 = 0) |  ~ (all_30_2_42 = 0)
% 224.30/173.14  																								|
% 224.30/173.14  																								| Instantiating formula (28) with xp, all_30_1_41, 0 and discharging atoms aNaturalNumber0(xp) = all_30_1_41, aNaturalNumber0(xp) = 0, yields:
% 224.30/173.14  																								| (1317) all_30_1_41 = 0
% 224.30/173.14  																								|
% 224.30/173.14  																								| Instantiating formula (28) with xn, all_30_2_42, 0 and discharging atoms aNaturalNumber0(xn) = all_30_2_42, aNaturalNumber0(xn) = 0, yields:
% 224.30/173.14  																								| (14340) all_30_2_42 = 0
% 224.30/173.14  																								|
% 224.30/173.14  																								+-Applying beta-rule and splitting (14338), into two cases.
% 224.30/173.14  																								|-Branch one:
% 224.30/173.14  																								| (14341)  ~ (all_30_1_41 = 0)
% 224.30/173.14  																								|
% 224.30/173.14  																									| Equations (1317) can reduce 14341 to:
% 224.30/173.14  																									| (197) $false
% 224.30/173.14  																									|
% 224.30/173.14  																									|-The branch is then unsatisfiable
% 224.30/173.14  																								|-Branch two:
% 224.30/173.14  																								| (1317) all_30_1_41 = 0
% 224.30/173.14  																								| (14344)  ~ (all_30_2_42 = 0)
% 224.30/173.14  																								|
% 224.30/173.14  																									| Equations (14340) can reduce 14344 to:
% 224.30/173.14  																									| (197) $false
% 224.30/173.14  																									|
% 224.30/173.14  																									|-The branch is then unsatisfiable
% 224.30/173.14  																				|-Branch two:
% 224.30/173.14  																				| (14346) aNaturalNumber0(all_0_7_7) = all_28_1_35 & aNaturalNumber0(xp) = all_28_2_36 & ( ~ (all_28_1_35 = 0) |  ~ (all_28_2_36 = 0))
% 224.30/173.14  																				|
% 224.30/173.14  																					| Applying alpha-rule on (14346) yields:
% 224.30/173.15  																					| (14347) aNaturalNumber0(all_0_7_7) = all_28_1_35
% 224.30/173.15  																					| (14348) aNaturalNumber0(xp) = all_28_2_36
% 224.30/173.15  																					| (14349)  ~ (all_28_1_35 = 0) |  ~ (all_28_2_36 = 0)
% 224.30/173.15  																					|
% 224.30/173.15  																					| Instantiating formula (28) with all_0_7_7, all_28_1_35, 0 and discharging atoms aNaturalNumber0(all_0_7_7) = all_28_1_35, aNaturalNumber0(all_0_7_7) = 0, yields:
% 224.30/173.15  																					| (1303) all_28_1_35 = 0
% 224.30/173.15  																					|
% 224.30/173.15  																					| Instantiating formula (28) with xp, all_28_2_36, 0 and discharging atoms aNaturalNumber0(xp) = all_28_2_36, aNaturalNumber0(xp) = 0, yields:
% 224.30/173.15  																					| (14351) all_28_2_36 = 0
% 224.30/173.15  																					|
% 224.30/173.15  																					+-Applying beta-rule and splitting (14349), into two cases.
% 224.30/173.15  																					|-Branch one:
% 224.30/173.15  																					| (14352)  ~ (all_28_1_35 = 0)
% 224.30/173.15  																					|
% 224.30/173.15  																						| Equations (1303) can reduce 14352 to:
% 224.30/173.15  																						| (197) $false
% 224.30/173.15  																						|
% 224.30/173.15  																						|-The branch is then unsatisfiable
% 224.30/173.15  																					|-Branch two:
% 224.30/173.15  																					| (1303) all_28_1_35 = 0
% 224.30/173.15  																					| (14355)  ~ (all_28_2_36 = 0)
% 224.30/173.15  																					|
% 224.30/173.15  																						| Equations (14351) can reduce 14355 to:
% 224.30/173.15  																						| (197) $false
% 224.30/173.15  																						|
% 224.30/173.15  																						|-The branch is then unsatisfiable
% 224.30/173.15  																			|-Branch two:
% 224.30/173.15  																			| (14357) aNaturalNumber0(xp) = all_33_1_50 & aNaturalNumber0(xm) = all_33_2_51 & ( ~ (all_33_1_50 = 0) |  ~ (all_33_2_51 = 0))
% 224.30/173.15  																			|
% 224.30/173.15  																				| Applying alpha-rule on (14357) yields:
% 224.30/173.15  																				| (14358) aNaturalNumber0(xp) = all_33_1_50
% 224.30/173.15  																				| (14359) aNaturalNumber0(xm) = all_33_2_51
% 224.30/173.15  																				| (14360)  ~ (all_33_1_50 = 0) |  ~ (all_33_2_51 = 0)
% 224.30/173.15  																				|
% 224.30/173.15  																				| Instantiating formula (28) with xp, all_33_1_50, 0 and discharging atoms aNaturalNumber0(xp) = all_33_1_50, aNaturalNumber0(xp) = 0, yields:
% 224.30/173.15  																				| (1298) all_33_1_50 = 0
% 224.30/173.15  																				|
% 224.30/173.15  																				| Instantiating formula (28) with xm, all_33_2_51, 0 and discharging atoms aNaturalNumber0(xm) = all_33_2_51, aNaturalNumber0(xm) = 0, yields:
% 224.30/173.15  																				| (14362) all_33_2_51 = 0
% 224.30/173.15  																				|
% 224.30/173.15  																				+-Applying beta-rule and splitting (14360), into two cases.
% 224.30/173.15  																				|-Branch one:
% 224.30/173.15  																				| (14363)  ~ (all_33_1_50 = 0)
% 224.30/173.15  																				|
% 224.30/173.15  																					| Equations (1298) can reduce 14363 to:
% 224.30/173.15  																					| (197) $false
% 224.30/173.15  																					|
% 224.30/173.15  																					|-The branch is then unsatisfiable
% 224.30/173.15  																				|-Branch two:
% 224.30/173.15  																				| (1298) all_33_1_50 = 0
% 224.30/173.15  																				| (14366)  ~ (all_33_2_51 = 0)
% 224.30/173.15  																				|
% 224.30/173.15  																					| Equations (14362) can reduce 14366 to:
% 224.30/173.15  																					| (197) $false
% 224.30/173.15  																					|
% 224.30/173.15  																					|-The branch is then unsatisfiable
% 224.30/173.15  % SZS output end Proof for theBenchmark
% 224.30/173.15  
% 224.30/173.15  172560ms
%------------------------------------------------------------------------------